2014-G12-Physics-E

Its m ain features are as follows: o 1. Hysteresis lb) H y t t w t H lo op of »ofl Iron O R » Rottntivrty T h e portion of O A of the curve is obtained when the O C ■ Cooreivtty magnetizing current / is increased and A R is the portion when the current is decreased. It may be noted that the value of flux f*B. density for any value of current is always greater when the current is decreasing than when it is increasing, i.e., magnetism lags behind the magnetizing current. This phenomenon is known as hysteresis.0^5223231 Th e magnetic flux density increases from zero and reaches a maximum value. A t this stage the material is said to be magnetically saturated. 3. R em anonco o r Retantivity W hen the current is reduced to zero, the material still remains strongly magnetized represented by point R on the curve. It is due to the tendency of domains to stay partly in line, once they have been aligned. 4- Coercivity To demagnetize the material, the magnetizing current is reversed and increased to reduce the magnetization to zero. Th is is known as coercive current represented by C on the cun/e. Th e coercivity of steel (Fig. 17.19 a), is more than that of iron as more current is needed to demagnetize it O nce the material is magnetized, its magnetization curve never passes through the origin. Instead, it forms the closed loop A C D C 'A . which is called hysteresis loop. 6. Area of the Loop Th e area of the loop is a measure of the energy needed to magnetize and demagnetize the specimen during each cycle of the magnetizing current. This is tho energy required to do work agBinst internal friction of the domains. Th is work, like all work that is done against friction, is dissipated as heat It is called hysteresis loss. Hard magnetic materials liko steel can not be easily magnetized or demagnetized, so they have large loop area as compared to soft magnetic material such as iron which can easily be magnetized. Th e energy dissipated per cycle, thus, for iron is less than for steel.150

S uita bility o t m a g n e tic m a te ria ls for different p u rp o s e s c a n be AM M noaM M M xM M t*studied b y taking the s p e c im e n through a co m p le te cycle a nd duo to magoobe ofloct. mo» •rtMfid ra w in g the h yste re sis lo o p . A m aterial w ith h*gh retentivity <t reduced to rrmlmum and *p**da n d la rge co e rc ive fo rce w o u ld b e m o st suitable to m a k e a can bo enhanced up to SOChnth'perm a ne n t m agn e t T h e co re s of e lectro m agnets used fora lte rnating c u rre n ts w h e re the s p e c im e n re pe a te dlyu n d e rg o e s m a g n e tizatio n a n d d e m a gne tiza tio n should ha ven a rro w h yste re sis c u rv e s of sm all a re a to m in im ize the w asteof energy. Esm m• Crystalline solids are those in which there is a regular arrangement of moieculos Th e neighbours of every molecule are arranged in a regular pattern that is constant through out the crystal. Thus, there is an ordered structure in crystalline solids.• In amorphous solids there is no regular arrangement of molecules. These are more like liquids with the disordered structure frozen in.• Polymers may bo said to be more or less solid materials with a structure that is intermediate between order and disorder. Theso can be classified as partially or poorty crystalline solids.• A crystalline solid consists of three dimensional pattern that repeats itself over and over again. This basic structure is called unit cell.• The force applied on unit area to produce any change in the shape, volume or length of a body is called stress.• When a long wire of length I with area of cross section A is being pulled by a force F, which results in an increase in length A I. the stress is catted tensile deformation.• When a small cylinder is subjected to a force F along the inward drawn normal to its area of cross section A to reduce its length, the stress is called compressive stress and deformation produced by it is called compressive deformation.• If a force F is applied tartgenttally to the surface of the opposite face of a cube to deform or twist it through an angle 0. the stress is termed as shear stress.• Strain is a measure of the deformation of a solid when stress is applied to it. In tho case of deformation in one dimension, strain is defined as the fractional change in length per unit length. Ifstrain is due to tensile stress, it is called tensile strain and ifit is produced as a rosult of compressive stress, it is tormed as compressive strain.• Th e ratio of stress to strain is a constant for a given matenal. provided the external applied force is not too great. This is called modulus of elasticity.• The strain energy can be obtained by tho area of the force-extonsion graph.• The electrical behaviour of semi-conductor is substantially changed on in tro d u c in g151

a sm all am ount of impurity into the pure sem i-conductor lattice. T h e process is called doping in w hich a small num ber of atom s of som e other suitable elem ents are added a s impurity. T h e doped sem i-conducting materials are called extrinsic• W h e n a silicon crystal is doped with a pentavalent elem ent, four vale nce electrons of the impurity atom form covalent bond with the neighbouring Si atom s, while the fifth valence electron provides a free electron in the crystal. S uch a doped or oxtrinsic semi-conductor is called n-type semi-conductor.• T h e re are so m e materials w ho so resistivity be com e s ze ro below a certain temperature T „ called critical temperature. B elow this temperature, such materials are called superconductors.• Substances in w hich the orbits and the spin axes of the electrons in a n atom are so oriented that their m agnetic fields support each other and the atom be haves like a tiny magnet are callod paramagnetic substances• T h e substances in w hich m agnetic fields produced by orbital and spin m olecules of the electrons add up to zero are called diamagnetic substances.• Substances in w hich the atoms co-operate with each other in such a w ay so as to exhibit a strong m agnetic effect are called ferromagnetic. G SSH 317.1 Distinguish between crystalline, am orphous and polym eric solids.17.2 Define stress and strain. W hat are their SI units? Differentiate betweon tensile, com pressive and shear m odos of stress and strain.17 3 Define m odulus of elasticity. S h o w that the units of m odulus of elasticity and stress are the sam e. A ls o discuss its three kinds.17.4 D ra w a stress-strain cu rve for a ductile material, a n d then define the terms: Elastic limit. Yield point a n d Ultimate tensile stress.17.5 W h a t is m eant b y strain en ergy? H o w can it be determ ined from the force-extension graph?17.6 D oscnbo the formation of energy bands in solids. Explain the difference am ongst electrical behaviour of conductors, insulators and sem i-conductors in terms of energy band theory.17.7 Distinguish between intrinsic and extrinsic sem i-conductors. H ow would you obtain n-type and p-type material from pure silicon? Illustrate it by schem atic diagram .17.8 Discuss the m echanism of electrical conduction by holes and electrons in a pure semi-conductor element.17.9 Write a note on superconductors.17.10 W hat is m eant by para, dia and ferromagnetic substances? G iv e exam ples for each.17.11 W h a t is m eant by hysteresis lo ss? H o w is it used in the construction of a transformer? 152

CHM 917.1 A 1.25 cm diameter cylinder is subjected to a load of 2500 kg. Calculate the stress on17.217.3 the barin mega pascals. (A ns: 200 MPa)17.417.5 A 1.0 m long copper wire is subjected to stretching force and its length increases by17.6 20 cm. Calculate the tensile strain and the percent elongation which the wire undergoes. (Ans:0.20.20% ) A wiro 2.5 m long and cross-section area 10 ’ m’ is stretched 1.5 mm by a force of 100 N in the elastic region. Calculate (i) the strain (ii) Young's modulus (iii) the energy stored in the wire. (A n s : 6.02 x 10M .66 x 10 :Pa, 7.5 x 10 \J) What stress would cause a wire to increase in length by 0 .0 1 % if the Young's modulus of the wire is 12 x 10\"5 Pa. What force would produce this stress if tho diameter of the wire is 0.56 m m ? (A n s : 1.2 x 10* Pa. 2.96 N) Th e length of a steel wire is 1.0 m and its cross-sectional area is 0.03 x 104mJ. Calculate the work done in stretching the wire when a force of 100 N is applied within the elastic region. Young's modulus of steel is 3.0 x 10'’ N m ! . (A n s : 5.6 x 1 0 5J ) A cylindrical copper wire and a cylindrical steel wire each of length 1.5 m and diameter 2.0 mm are joined at one end to form a composite wire 3.0 m long. Th e wire is loaded until its length becomes 3.003 m. Calculate the strain in copper and steel wires and the force applied to the wire. (Young's modulus of copper is 1.2 x 10\" Pa and forsteel is 2 .0 x 1 0 \" Pa). (A n s : 1.25x 10°. 7.5x10'*. 477 N ) 153

b z q q )1 8 ELECTRONICS Learning Objectives At the end of this chapter the students will b e able to: Describe forward and resen/e biasing of a p -n junction. 2 Understand half and full wavfe rectification. K now the uses of light emitting diode, photo diode and photo voltaic cell. 4 Describe the operation of transistor. 5 K n o w current equation and solve related problems. 6 Understand the use of transistors as an amplifier and a switch. 7 Understand operational amplifier and its characteristics. K n o w the applications of an operational amplifier as inverting and non-inverting amplifier using virtual ground concept. 9 Understand the use of an operational amplifier as a comparator e .g .. night switch. 10. Understand the function of each of the following logic gates: A N D . N O T . O R and N A N D gates and represent their functions by m eans of truth tables (limited to a m axim um of two inputs). 11. Describe how to com bine different gates to form X O R and X N O R gates. 12 Understand combinations of logic gates to perform control functions. T he huge advances in electronics over the recent past are due to discovery and use of sem i-conductors. Silicon is one of the most com m only used semi-conductors, and is the basic material from which highly sophisticated integrated circuits known as 'chips' are m ade. T h e use of chips in analogue as well as in digital electronics is described in the form of the black boxes. Th is chapter is based on the preliminary concepts introduced in the secondary school physics course. 18.1 B R IE F R E V IE W O F p -n J U N C T IO N A N D IT S C H A R A C T E R IS T IC S A p -n junction is formed when a crystal of germ anium o r silicon is grown in such a w a y that its one half is doped with a trivalent impurity and the other half with a pentavalent impurity. O n e of the m ost important building blocks of electronic devices is the p-n junction. Its n-region contains free electrons as majority charge carriers and p-region contains holes as majority charge carriers. Just after the formation of the junction, the free electrons in the n-rcgion. because of their random motion, diffuse into the p-region. A s a result of this diffusion, a region is formed around the junction in which charge carriers are not present. Th is region is known as depletion region (Fig. 18.1 a ). In this figure, bkic dots represent the free electrons and the small circles show the holes whereas the circles wilh ♦ and - signs show the positive and negative ions which constitute the depletion region. D ue to charge on 154

p-r«gion n-rc^oo these ions a potential difference develops across the ;: : :7 a depletion region (Fig. 18.1 b). Its value is 0.7 V in case of silicon and 0.3 V in case of germanium. This potential ¥■ difference, called potential barrier, stops further diffusion of electrons into the p-region. • -whp-typo ■ ♦| / Forw ard Biased p -n Junctio n (a) L convention* — 'W hen an external potential difference is applied across a p-njunction such that p-side is positive and n-side is negative,then this external potontial difference supplies energy to freee le c t r o n s in th e n -r e g io n a n d to h o le s inp-region. When this energy is sufficient to overcome thepotential barrier, a current of the order of a few miliamperesbegins to flow across the p-n junction. In this state the p-njunction is said to be forward biased (Fig. 18.2 a). Th evariation of current through the junction with the bias voltagecan be studied by the circuit shown in Fig. 18.2 (b). Th e valueof current for different values of bias voltage is noted and a-current-bias voltage graph is plotted. Fig. 18.3 shows thegraph for a typical low power silicon diode. As shown in Fig. 18.3. if forward bias voltage is increased byA V.. the current increases by m , . Th e ratio AV./A/,is known as forward resistance of the p-n junction, i.e..r,*-■A*/,■ ( 18.1 )It is the resistance offered by the p-n junction when it isconducting. Th e value of r, is only a few ohms.Reverse Biased p-n Junctio nW hen the external source of voltage is applied across a cFuI9rre1n8t t2hrTohug0rnotn»e an jppro&Jt*)p-n junction such that its positive terminal is connected to n- *ode w*>on theregion and its negatrvo terminal to p-region. the p-n junction d & t o ( t to rm w j t»*V X lis said to be reverse biased (Fig. 18.4). In this situation nocurrent flows due to the majority charge carries. However avery small current, of the order of few microamperes flowsacross the junction due to flow of minority charge carriers(F ig .18.4). It is known as reverse current or leakage current.Th e variation of reverse current with the applied bias voltagecan be studied by the circuit shown in F ig .18.5. Fig.18.6shows the revorse characteristic for the p-n junction. It can beseen that as the reverse voltage is increased from 0. thereverse current quickly rises to its saturation value /„. A s thereverse voltage is further increased, the reverse current 155

<Hyp* remains almost constant. Here the resistance offered by the diode is very high - ofthe order of several mega ohms.Flg.18.4 UrxJw a raveryo) bowod A s the reverse voltage is increased, the kinetic energy of thecondition tn w a n afmoat no Currem minority charge carriers with which they cross the depletion^ n o u g h t-* diode region also increases till it is sufficient to break a covalent bond. As the covalent bond breaks, more electron-hole pairs are created. Thus, minority charge carriers begin to multiply due to which the reverse current begin to increase till a point is reached when the junction breaks down and reverse current rises sharply (F ig .18 6 ) After breakdown the reverse current will rise to very high value which will damage the junction. P -n junction is also known as a semi-conductor diode whose symbolic representation is given in Fig.18.7. Th e arrow head represents the p - region and is known as anode. The vertical line represents the n-region and is known as cathode. The current flows in the direction of arrow when the diode is forward biased. 18.2 R E C TIF IC A TIO NReverie Ban Conversion of alternating current into direct current is called•25y -20/ -IS v -1CX -5v rectification. Semi-conductor diodes are extensively used for 10i.A this purpose. There are two very common types of rectification. 25 uA (i) Half-wave rectification and (ii) Full-wave rectification i 50 11A H a lf-W a v e R e c tific a tio n t * 1- ' A half-wave rectification is shown in F»g. 18.8 where an alternating voltage of period T called input voltage is applied Flfl. 18.7 to a diode D which is connected in series with a load resistance R. In this method only one half of alternating 0 current cycle is converted into direct current.HWP* During the positive halfcycle of the input alternating voltage i.e.. (•) during the interval 0 -> 772. the diode D is forward biased, so it offers a very low resistance and current Bows through R. The flow ofcurrent through R causes a potential drop across itwhich varies »n accordance with the alternating input (Fig. 18.8 c).0 T0 ........m During the negative half cycle i.e.. during the period 772 -> T. the diode «s reverse biased. Now it offers a very high<b) \ J \ resistance, so practically no current flows through R and potential drop across it is almost zero (Fig. 18.8 c). The same0 rn r^ \ events repeat during the next cycle and so on. The current(e) Fig.18.8 through R flows in only one direction which means it is a direct current. However, this current flows in pulses (Fig. 18.8 c). The 156

voltage which appears across load resistance R is known as u*output voltage. 1*10 Full-W ave RectificationW e have seen that in a half-wave rectification, only one half ofthe alternating input voltage is used to send a unidirectionalcurrent through a resistance. However both halves of the inputv o l t a g e c y c l e c an be u ti l iz e d u si ngfull-wave rectification. Its circuit consists of four diodesconnected in a bridge typo arrangement (Fig. 18.9). Tounderstand the operation of tho circuit, recall that a diodeconducts only when it is forward biased. During the positivehalf cycle, i.e.. during tho time 0 772, the terminal A of thebridge is positive with respect to its other terminal B. Now thediodes D. and D „ become forward biased and conduct. Acurrent flows through the circuit in the direction shown byarrows in Fig. 18.9 (a). During the negative half cycle, i.e..during the time interval 772 -> T, terminal A is negative and B ispositive. Now the diodes D. and D, conduct and current flowsthrough the circuit in the path shown by arrows in Fig. 18.9 (b).By comparing Figs. 18.9 (a) and 18.9 (b). it can be seen thatdirection of current flow through the load resistance R is thesame in both the halves of the cycle. Thus both halves of thealternating input voltage send a unidirectional current throughR. The input and output voltages are shown in Fig. 18.10.However the output voltage is not smooth but pulsating. It canbe made smooth by using a circuit known as filter.18.3 S P E C IA L L Y D ES IG N ED p-n JU N C TIO N SIn addition to the use of semi-conductor diode as rectifier,many types of p-n junctions have been developed for specialpi rocses. Three most commonly used such diodes are (i) Light emitting diode (ii) Photodiode (iii) Photo voltaic cellLight Em itting DiodeLight emitting diodes (L E D ) are made from specialsemi-conductors such as gallium arsenide and galliumarsenide phosphide in which the potential barrier between pand n sides is such that when an electron combines with ahole during forward bias conduction, a photon of visiblo lightis emitted. These diodes are commonly used as small light 157

sources. A specially formed array of seven LEO 'S is used for displaying digits etc.. in electronic appliances (Fig. 18.11). Q A MV«1 segment dopiay Photo Diodeu ! c 3 H 5 6 >89 Photo diode is used for the detection of light It is operated in the reverse biased condition (Fig. 18.12 a). A photo diode sym bol is shown in Fig. 18.12 (b ). W h en no light is incident F I s -18.12 o n the junction, the reverse current / is almost negligible butFig. 18. 13 w hen its p -n junction is exposed to light, the reverse current increases w ith the intensity of light (F ig . 18 .12 c). A photo diode can turn its current O N and O F F in nano-seconds. H ence it is one of the fastest photo detection devices.Applications of photo diode include Detection of both visible and invisible radiations ii Automatic switching in Logic circuits iv. Optical communication equipm ent etc. Photo-V oltaic C o ll. It consists of a thick n-type region covered by a thin p-type layer. W hen such a p-n junction having no external bias (F ig .18.13). is exposed to light, absorbed photons generate electron-hole pairs. It results into an increase percentage of minority charge carriers in both the p and n-regions and w hen they diffuse close to the junction, the electric field due to junction potential barrier sw eeps them across the junction. It causes a current flow through the external circuit R. Th e current is proportional to intensity of light. 158

18.4 TR A N S IS T O R SA transistor consists of a single crystal of germanium or E csilicon which is grown in such a way that it has three regions C(Figs.18.14 8,18.15).In Fig. 18.14 the central region is p type which is sandwiched E F lfl 18.14between two n type regions It is known as n-p-n transistor InFig.18.15. the n type central region is sandwiched between Etwo p type regions. It forms a p-n-p transistor. The central —» cregion is known as base and the other two regions are calledemitter and collector. Usually the base is very thin, of theorder of 10'4 m. The emitter and collector have greaterconcentration of impurity. The collector is comparativelylarger than the emitter. The emitter has greater concentrationof impurity as compared tothe collector.It can be seen in Figs.18.14 and 18.15 that a transistor is a Flfl 18.15combination of two back to back p-n junctions: emitter-basejunction and collector-baso junction. EC BFor normal operation of the transistor, batteries V „ and ______ Flfl. 18.15are connected m such a way that its emitter-base junction isforward biased and its collector base junction is reverse s R.biased. Vw Is of much higher value than V „ . Fig. 18.16 showsthe biasing arrangement for n-p-n transistor when thetransistor has been represented by its symbolic form.Fig.18.17 shows the same fora p-n-p transistor. — -----It may be noted that polarities of the biasing batteries VM and are opposite in the two types of tho transistors. In actualpractice, itis the n-p-n transistor that is generally used. So wewill discuss n-p-n transistors only. 159

C u rre n t F lo w in a n -p -n Tra n s is to rFig, 18.18 (a) shows a n-p-n transistor at the instant when thebiasing voltage is applied. Electrons in the emitter, shown byblack dots, have not yet entered the base region. After theapplication of the biasing voltage, omitter base junction isforward biased, so emitter injects a large number of electronsin base region (Fig. 18.18 b). These free electrons in the basecan flow in either of two directions. They can either flow out ofthe base to the positive terminal of V „ or they can beattracted towards the collector bocause of battery V ^ . Sincethe base is extremely thin, very few electrons manage torecombine with holes and escape out of the base. Almost allof the free electrons injected from the emitter into the baseare attracted by the collector due to it large positivepotential (Fig 18.18 c). Thus, in a normally biasedtransistor due to above mentioned flow of electrons, we cansay. that an electronic current /,. flows from the emitter intothe base A very small part of it. current /,. flows out of thebase, the rest of it /c flows out of the collector (Fig. 18.19). Fig. 18 19T h e flow of conventional current is shown in Fig. 18.20. Infuture we will use conventional current only. From the figure,it can be seen that /,=/c*/. (182I A s very few electrons flow out of baso. so /, is very small as r, compared to/c.It is also found that for a given transistor the ratio of collectorT- current /cto base current /, is nearly constant i.e., (1 8 3 ) is. '8T h e ratio [J is called current gain of transistor. Its value is quitelarge - of the order of hundreds. Eqs.18.2 and 18 3 are

fundamental equations of all transistors.Example 18.1: In a certain circuit, the transistor has acollector current of 10 m A and a base current of 40 >iA. Whatis the current gain of the transistor?Solution: lO x lO lA ^S O /B 4 0 x 1 0 A18.5 T R A N S IS T O R A S A N A M P L IF IE RIn majority of electronic circuits, transistors are basicallyused as amplifiers. An amplifier is thus the building block ofevery complex electronic circuit. It is for this reason that studyof transistor amplifier is important.Th e circuit in Fig. 18.21 is a transistor voltage amplifier. Thebattery V „ forward biases the base-emitter junction andreverse biases the collector-base junction. V „ and V „ arethe input and output voltages respectively. T h e base currentis /, = v*/r. where r . is base emitter resistance of thetransistor. T h e transistor amplifies it p times. So/c = P/n= p V „ / r .T h e output voltage V . = V c, is determined by applying KVLequation in the output loop which givesVcc^cRc +V* or V ct = V cc-/c R<Substituting the value of lcand replacing by VsV ',=V oc-p V MRc/r. 18.4(a)W hen small signal voltage AV„ is applied at the inputterminal B. the input voltage changes from V „ to V „ ♦ A V,.Th is causes a little change in base current from /, to (/, + A /,)due to which the collector current changes from /cto (/c + AA).A s the collector current changes, the voltage drop across Rei.e. (/cRc) also changes due to which tho output voltageVa changes by AV*. Substituting the changed values inEq. 18.4(a)V. + A V .s V ^ -p (V « + A V JR c/r, ............. 18.4(b)Subtracting Eq. 18.4(a)from Eq. 18.4(b) A V , = -p A V ’>>Rc/ r. 161

Therefore the gain of the amplifier A = A V JA V,= p R</r.Th e value of the factor p f V r. is of tho order of hundreds, sothe input voltage is amplified. Th e negative sign shows thatthere is a phase shift of 180 between the input and theoutput signals. 18.6 T R A N S IS T O R A S A S W ITC HFig. 18.22 (a ) shows the circuit in which a transistor is used asa switch. Th e collectors C and emitter E behave as theterminals of the switch. Th e circuit in which the current is to betuned O F F and O N . is connected across these terminals.T h e base B and emitter E act as control terminals whichdecide the state of the switch.In order to turn on the switch, a potential V , is appliedbetween control terminals B E (Fig. 18 22 a). This injects alarge current /, into the base circuit due to which a very heavycurrent /c begins to flow in the C E circuit. This large value ofcollector current is possible only when the resistancebetween C and E drops down to such a small value that thepotential drop across C E is nearly 0.1 volt. In Fig. 18.22 (a)emitter is at ground, so we can assume that collector is alsoat ground and collector emitter circuit of Fig. 18.22 (a ) can bedrawn a s shown in Fig. 18.22 (b). C E switch is closed and thebulb glows due to flow of large collector current. To turn theswitch O F F the base current /, is set zero by opening thebase circuit (Fig. 18.22 c). As /c = p /». so /c becomes zeroand C -E circuit becomes open (Fig. 18.22 d ) Now theresistance between C and E becomes nearly infinity whichopens the C E switch.A n electronic computer is basically a vast arrangement ofelectronic switches which are made from transistors. 18.7 O P E R A T IO N A L A M P L IF IE RA s stated earlier, amplifier is an important electronic circuitthat is used in almost every electronic instrument. So insteadof making amplifier circuit by discrete components, the wholeamplifier is integrated on a small silicon chip and enclosed ina capsule. Pins connected with working terminals such asinput, output and power supply project outside the capsule(Fig. 18.23 a). T h e enclosed circuit of the amplifier is used bymaking requisite connections with these pins. Such an

integrated amplifier is known as operational amplifier(op-am p). as it is som e times used to perform mathematicaloperations electronically.The op-amp is usuaty represented by its symbol shown inFig.18.23 (b). It has two input terminals One is kno\n asinverting input (-) and the other non-inventing input (♦). A signalthat is appled at the inverting (-) input, appears after amplification,at the output terminal with a phase shift of 180° (Fig. 18.24 a). Itcan be seen that the signal is inverted as itappears at the output.This is why this terminal is known as inverting. If the signal isapplied at non-inverting input (+), it is amplified at the outputwithout any change of phase (Fig. 1824 b). input F ig. 18 24Characteristics of op-amAn op-am p has a large number of characteristic parameters. Fig. 18.25W e will discuss only three of them. Fig. 18.28 Fig. 18.27(i) Input ResistanceIt is the resistance between the (♦ ) and ( - ) inputs of theamplifier (Fig. 18.25). Its value is very high -- of the order ofseveral mega ohms. D ue to high value of the input resistanceR r . practically no current flows between the two inputterminals. It is a very important feature ofop-amps.(II) Output ResistanceIt is the resistance between the output terminal and ground(Fig. 18.26). Its value is only a few ohms.(iii) Open Loop GainIt is the ratio of output voltage V, to the voltage differencebetween non-inverting and inverting inputs when there is noexternal connection between the output and the inputs(Fig. 18.27)i.e.. r(18.5) A* V, - V V, 163

Th e open loop gain of the amplifier is very high. It is of the order of 10’. 18.8 O P -A M P A S IN V E R T IN G A M P L IF IE R Fig. 18.28 shows the circuit of an op-am p when used as an inverting amplifier. T h e input signal Vm which is to be amplified, is applied at inverting terminal ( - ) through a resistance R,. V„ is its output. Th e non-inverting terminal (♦) is grounded, i.e.. its potential is zero. W e know that A * isv. very high, of the order of 10’ . A s Vr m ay have any value between ♦Vc’ c (+ 1 2 V ) and - V,K (-1 2 V ) so according to Eq.18.5. for finite (±12V) value of V,. V . - V . - 0 or V. • V.. Since V. is at ground so V is virtually at ground potential i.e.. V. * 0. Referring to Fig. 18.28. Current through R, * Current through R 2mJ2 A s practically no current flows between (-) and (♦ ) terminals, so accordingto Kirchhoffs current rule /, = /,As V J R1 R* V R1 is defined as gain G of tho inverting amplifier, so G m— R ............. (18.6) R1Th e negative sign indicates that the output signal is 180* outof phase with respect to input signal. It is interesting to notethat the closed loop gam depends upon the two oxtemallyconnected resistances R , and R }. Th e gain is independent ofwhat is happening inside the amplifier.IfR , = 10 k O and R , = 100 kO. the gain ofthe amplifier is ° R 10U218.9 O P -A M P A S N O N -IN V E R TIN G AM P LIFIERTh e circuit diagram of op-am p as non-inverting amplified isshown in Fig. 18.29. In this case the input signal V , is appliedat the non-inverting terminal (♦)• As explained earlier, due tohigh open loop gain of amplifier, the inverting (-) and non

inverting (♦ ) inputs are virtualty at the same potential. That is. V. * V. = Vm For Your InformationAlso, from Fig. 18.29. An op a m p - The c*cutt in the buck boxCurrent through R 0 -V . o-v. -y, R1 R1 R1Current th ro u g h ^ . V ~ V o V „-V . \",A s practically no current flows between (-) and (+ ) terminals,so by Kirchhoffs current rule /, = /,Hence - v „ v.-v. R1 R, f_L + 0 . Galn=^ \" U I f (18.7)Again the gain of the amplifier is independent of the internalstructure of the op-amp. Itjust depends upon the two externallyconnected resistances R, and R,. Th e positive sign of gainindicates that the input and out put signals are in phase.Example 18.2: Find the gain of the circuit as shown inFig.18.30.Solution:A s the input signal V . is connected to non-inverting input(♦ ). so the op -a m p acts as a non-inverting amplifier.Com paring it with the circuit of non-inverting amplifier asshownin Fig. 18.29,w ehave R , = infinity and R,= 0 Gain18.10 O P -A M P A S A C O M P A R A T O R F*. 1S.J1Op-am p usually requires two power supplies of equal voltagebut of opposite polarity. Most op-am p operate with VCC* ± 1 2 Vsupply (Fig. 18.31). 165

A s the open loop gain of the op-amp is very high (10*). even a very small potential difference between the inverting and non­ inverting inputs is amplified to such a large extent that the amplifier gets saturated, i.e.. its output either becomes equal to ♦V,* or -Vet.. This feature of op-amp is used to compare two voltages. Fig. 18.32 shows the circuit of an op-amp used asIntegrated circuit (* C ) c N p » are comparator. V, is reference voltage which is connected withmanufactured o n water* o » *erm- (♦ ) terminal and V is the voltage which is to be compared witheonductor materiel the reference V,. It is connected with (-) terminal. Whon V > V. or V > V 9. thon V,= -V’a. and if V < V . or V < V „ then V .*+V 'ce 18.11 C O M P A R A T O R A S A N IG H T S W IT C H Suppose it is required that when intensity of light fads below a certain level, the street light is automatically switched on. This can be accomplished by using op-am p as a comparator. In Fig.18.33 resistances R , and ft, form a potential divider. Th e potential drop across R, provides the reference voltage V , to the (+ ) input of the op-amp. Thus R, +Rj (18.8) L D R is a light dependent resistance. T h e value of its resistance R l depends upon the intensity of light falling upon it. R , and R , form another potential divider. T h e potential drop across R , is V which is given by V ' - R~' r - x- VV crc. (18.9) V provides the voltage to ( - ) input of the op-amp. V w ill not be 166

a constant voltage but it will vary with the intensity of light.During day time, when light is falling upon LDR, R, is small.According to Eq.18.9. V ’ will be large such thatV > V, so that V .= - Vcc. Tho output ofthe op is connected witha relay system which energizes only when V , = ♦Va and thenit turns on the street lights. Thus when V . ■ •V ^. the light willnot be switched O N.As it gets darker. Rl becomes larger and Vdecreases. WhenV becomes just less than V,. the output of op-amp switchesto +Vccwhich onergizes the relay system and the street lightsare turned ON.18.12 D IG ITA L S Y S TE M SA digital system deals with quantities or variables which haveonly two discrete values or states. Following are theexamples ofsuch quantities.(i) Aswitchcanbeeitheropenorcloscd.(h) The answer of a question can be either yes or no.( mi) Acertain statement can be eithertrue or false.(rv) A bulb can be either offor on.Various designations are used to represent the twoquantized states of such quantities. The most common ofthese are listed in Table 18.1. Ta b le 18.1One of the states 1 2 34 56The other state True High 1 Yes On Closed False Low 0 No Off OpenMathematical manipulation of these quantities can be bestcarried ifthey are represented by binary digits 1 and 0. Whenwe are dealing with voltages, designation No.2 is also aconvenient representation.In describing functions of digital systems a closed switch willbe shown as 1 and open switch will be shown as 0. Similarly,a lighted bulb will be described as 1 and an off bulb will bedescribed as 0.Just as we require two basic mathematical operations, i.e..addition and subtraction for the mathematical manipulation 167

of ordinary quantities which can possess all continuous values, w e require a special algebra, known as Boolean algebra for the manipulation of the quantities which have values 1 and 0. now designated as Boolean variables. Boolean algobra is based upon three basic operations nam ely r A N D operation, (i O R operation and (in) N O T operation. You have already read about these operations. Hero w o would study about logic gates which implement these operations. 18.13 FU N D A M EN TA L LO G IC G A TE S Fig. 18.34 T h e electronic circuits which implement the various logic operations aro known as logic gates. In those gates the highlnpo,A - ) __ ' and low states, i.e.. 1 and 0 states are simulated b y certain voltago levels. Ideally one particular voltage level representsInput B • a high (1 ) and another voltage level represents a low (0 ). In practical digital circuits, how ever a 1 or high can be any OR «8I« voltage between a specified m inimum value and a specified Fig. 18.35 maximum valuo. Likewise 0 or low can bo any voltage between a specified m inimum and a specified maximum. Fig. 18.34 show s the range 1 and 0 levels for a certain typo of digital gates. Th u s if voltage of 3.5 V is applied to a gate, it will accept it a s high or 1. If a voltago of 0.5 V is applied, the gate x will recognize it as 0 or low. O R Gate O R gate as sym bolically represented in Fig. 18.35. implements the logic of O R operation. It has two or more inputs and a single output X. Th e output has a value 1 when at least one of its inputs A and B is at 1. Th u s X will b e zero—5 ! only when both the inputs are 0. Th u s it implements the truth table of O R operation (Table 18.2). Th e mathematical notation for O R operation isI n p u t A * ---------------- t Ompui X =A ♦ BInputB * - 4 X A N D Gate | AM ) 8»1o T h e A N D gate show n in Fig. 18.36 has two or m ore inputs and a single output. It is designed such that it implements the Ftg. 18.38 truth table of A N D operation, i.e.. its output X is 1 only when T»W* 18.3 both of its inputs A and B are at 1 and for all other combinations of the values of A and B. X is zero X (Table 18.3). T h e mathematical notation forA N D operation is X =A .B 168

N O T Gate N O T g .v * F 19 . 16.37It performs the operation of inversion or complementation.That is why it is also known as inverter. It changes a logic TaM* 18Alovel toits opposite level, i.e.. itchanges 1 toO and 0 to 1 Thesymbolic representation of N O T gate is shown in Fig. 18.37. mWhenever a bar is placed on any variable, it shows that thevalue of the variable has been inverted. For example1 * 0 and 0 * 1. The 'bubble' (o) in Fig.18.37 indicatesoperation of inversion. Its truth table is given in Table 18.4.The mathematical notation for N O T operation is X = A18.14 O T H E R LO G IC G A T E SIn NO R gate the output of OR gate is inverted. Its symbol is InputA • OM pUshown in Fig.18.36 and its truth table is given inTable 18.5. The mathematical notation for NOR operation is Input 8 N AN D Gate won 9M0In NAND gate the output of an AN D gate is inverted. Itssymbol is shown in Fig. 18.39. The bubble in this figure F ig . 18.38shows that the output ofAND gate is inverted. The truth tabloimplemented by it is shown in Table 18.6. The mathematical * -f - r -o ^notation for NAND operation is 01_ . .101 1 0 X= A .BExclusivo O R Gate(XOR) _ _09Consider a Boolean function X of two variables A and B such mpu«A * -that X = A B * A B Input B • -The first term of tho function X is obtained by ANDing the NANOgMavariable A with N O T of B. The second term is N O T of A F ig 18.39ANDed with B. The function X is obtained by ORing these twoterms. It can be constructed by combining AND. O R and N O T A e 6vtt>utgates according to tho scheme shown in Fig. 18.40(a). The 0 01 6 1 1 0 1 1 .. 1 ._— 0 H > ^D — l D -*F ig . 18.40 (a ) M aking a n XOR g ate 169

m£m value of this function can be obtained by drawing the truth tabte (Tabte 18.7) which gives the value of X for all the values — 5\" of the vanabtes A and B. The value of X is 0 when the two inputs have the same values and it is 1 when the inputs havempotA I >r - - ^^ different values. It can be verified that the circuit of Fig. 18.40 (a) implements this truth table. The symbol of XOR;3Input B W gate is shown in Fig. 18.40(b). X O R gam Exclusive - NOR gate (X N O R ) F ig . 18.40 (b )input A The exclusive N O R gate is obtained by inverting the outputInput B ofaX OR gate. Its symbol is shown in Fig. 18.41. The bubble XN O R g*M Fig. 1841 Oujpoi shown at the output in this figure shows that the output of # X XO R gato has been inverted. So its Boolean expression is given by X= A B*AB T .M .1 8 J The truth table of XNOR gate is given in the Table 18.8. Its output is 1 when its two inputs are identical and 0 when the two inputs are different. Like XO R gate, it is also constructed by a combination of NO T. AN D and NOR gates by the scheme shown in Fig. 18.42.SI -p » a £ ) AB AB F lfl. 18.42 1 8 .1 5 A P P L IC A T IO N S O F G A T E S IN C O N T R O L SYSTEM S Gates are widely used in control systems. They control the function of the system by monitoring some physical parameter such as temperature, pressure or some other physical quantity of the system. As gates operate with electrical voltages only, so some devices are required which can convert various physical quantities into electric voltage. 170

T h e s e de vices are know n as sensors. For exam ple, in the FIexam ple of night switch. Light Dependent Resistance (L D R )is a se n so r for light b e c a u s e it c a n convert c h a n g e s in theintensity of light into electric voltage. A thermistor is a sensorfor tem perature. A m icrop ho ne is a sound sensor. Sim ilarlythere are lovel sensors which give an electrical signal w henthe level of liquid in a vesse l attains a certain limit. O n e suchapplication is descnbed hero. For exam ple sensors are usedto m onitor the pressure and tem perature of a chem icalsolution stored in a vat. T h o circuitry for e a ch sensor is suchthat itp r o d u c e s a H IG H .i.e .. 1 w h e n either the tom porature orpressure exceed s a specified value. A circuit is to bede sign e d w h ich will ring a n alarm w h e n either thetem peraturo or pressure or both cross the m axim umspecified limit. T h e alarm requires a L O W (O ) voltage for itsactivation.T h e block d ia g ra m of the prob le m is s h o w n in Fig. 18.43 inw h ich C is the circuit to be de sign ed . Its inputs A and B a re fedb y the tem peraturo and pre ssure sensors T a n d P fitted intothe vat. W h e n e v e r output of the circuit C is L O W . the alarm isactivated S o the circuit C should be such that its output is 0as soon as tho limit for tem perature or pressure is exceeded,i.e.. w h e n A = 0 . B = 1 or w h e n A = 1. B = 0 o r w h e n A = B = 1.T h e output of C should be H IG H w hen tem perature andprossure are within the specified limit, i.e., w h e n A = B = 0.T h is g iv e s th e truth table 18.9 w hich the circuit C has toim plem ent. It c a n b e seen that it is the truth table of N O Rgate. S o the circuit C in Fig. 18.43 should be a N O R gate ass ho w n in Fig. 18.44. gos When an external potential difference is applied across a p-n junction such that p-side is positive and n-side is negative, it is called forward biased. When the external source of voltage is applied across a p-n junction such that its positive terminal is connected to n-region and its negative terminal to p- region, the p-n junction is said to be reverse biased. Conversion of alternating current into direct current is called rectification. When only one half of alternating current cycle is converted into direct current, it is called half-wave rectification.• Transistor is a semiconductor device consisting of threo electrodes, namely emitter, base and collector. For normal operation, the base-emitter junction is forward biased whereas the collector-base junction is reverse biased.171

Input resistance is the resistance between the positive and negative inputs of the amplifier. O utput resistance is the resistance between the output terminal and ground. Instead of making amplifier circuit by discrete components, tho whole amplifier is integrated on a small silicon chip and enclosed m a capsule. Pins connected with working terminals such as inputs, outputs and power supply project outside the capsule. Such an integrated amplifier is known 3S operational amplifier. O pe n loop gain is the ratio of output voltage and the difference between non­ inverting and inverting inputs w h en there is no external connection betw een the outputs and inputs. A digital system deals with quantities or vahabtos which have only two discrete values or states. T h e electronic circuits which implement the various logic operations are known as logic gates. M lld A d M H J18.1 H o w does the motion of an electron in a n-typo substance differ from the motion of holes in a p-type substance?18.2 W h at is the net charge on a n-type or a p-type substance?183 T h e anode of a diode is 0.2 V positive with respect to its cathode. Is it forward biased?18.4 W h y charge carriers are not present in the deplotion region?18.5 W hat is the effect of forward and reverse biasing of a diode on the width of depletion region?18.6 W h y ordinary silicon diodes do not emit light?18.7 W h y a photo diode is operated in reverse biased state?18.8 W h y is the baso current in a transistor very small?18.9 W hat is the biasing requirement of the junctions of a transistor for its normal oporation? Explain how these requirements are m et in a com m on emitter amplifier?18.10 W hat is the principle of virtual ground? A pply it to find the gain of an inverting amplifier.18.11 Th e inputs of a gate are 1 and 0. Identify the gate ifits output is (a) 0. (b) 118.12 Tick ( )the correct answer(•> A diode characteristic curve is a plot between (a) current and time (b) voltage and time (c) voltage and current (d) forward voltage and reverse voltage 172

Th e cotour of light emitted by a L E D depends on (a ) its forward bias (b ) its reverse bias (c ) the amount of (d ) the type of semi-conductor forward current material used. In a half-wave rectifierthe diode conducts during a. both halves of the input cycle b. a portion of the positive halfof the input cycle c. a portion of the negative half of the input cycle d O ne half of the input cycle(iv) In a bridge rectifierof Fig. Q . 18.1 when V is positive at point B with respect to pointA . which diodes are O N . D , and D4 D. and D, D , and D, D, and D, Th e com mon emitter current amplification factor p is given by a. c. d. FI#. Q. tt.1(vi) Truth table of logic function(vii) a summarizes itsoutput values(viii)(ix) b. tabulates all its input conditions only c. display all its inpul/output possibilities d. is not based on logic algebra Th e output of a two inputs O R gate is 0 only when its a. both inputs are 0 b. either input is 1 c. both inputs are 1 d. either input is 0 A tw o inputs N A N D gate with inputs A and B has an output 0 if a. AisO b. BisO c. bothA and B a re zero d. both A a n d Bare 1 Th e truth table shown below is for a .X N O R g a te b. O R gate c. A N D gate d. N A N D gate 173

I S fiH W .t a18.1 T h e current flowing into the base of a transistor is 100 pA. Find its collector current /c. its emitter current /, and the ratio IJ I , . ifthe value of current gam p is 100. (A n s : 10mA. 10.1 mA. 0.99)18.2 Fig.P.18.2 shows a transistor which operates a relay as the switch S is closed. Th e relay is energized by a current of 10 m A. Calculate the value R , which will just make the relay operate. The current gain p of the transistor is 200. W hen the transistor conducts, its V „ can be assumed to be 0.6 V. (A n s : 168 kO)18 3 In arcurt (Fig.P.18.3). there is negligible potential drop between B and E . if. P is 100. Calculato (i) base current (ii) collector current (ini potential drop across R c (iv) Va . (A n s : 11.25 pA. 1.125 mA. 1.125 V. 7.875 V )18.4 Calculate the output of the op-amp circuit shown in Fig.P. 18.4. (Ans: 0)18. 5 Calculate the gam of non-invertmg amplifier shown in Fig.P.18.5. (Ans: 5) rie. p. u s 174

DAWN OF MODERN PHYSICSLearning ObjectivesAt the end of this chapter the students will be able to:1. Distinguish between inertial and non-mertial frames of references.2. Descnbe the postulates of special theory of relativity and its results.3. Understand the NAVASTAR navigation system.4 Understand the concept of black body radiation.5. Understand and describe how energy is distributed over the wavelength range for several values of source temperature.6. Know Planck’s assumptions.7. Know the origin of quantum theory.8. Show an appreciation of the particle nature of electromagnetic radiation.9. Descri be the phenomenon of photoelectric effect.10. Explain photoelectric effect in terms of photon energy and work function.11. Explain the function of photocell and descnbe its uses.12. Describe Compton's effect.13. Explain the phenomena of pair production and pair annihilation.14 Describe de-Broglie’s hypothesis of wave nature of particles15. Describe and interpret qualitatively the evidence provided by electron diffraction for the wave nature of particles.16. Understand tho working principle of electron microscope17. Understand and describe uncertainty principle.In the early part of the twentieth century, many experimental and theoretical problemsremained unresolved. Attempts to explain the behaviour of matter on the atomic level withthe laws of classicalphysics were not successful. Phenomena such as black body radiation,the photoelectric effect, the emission of sharp spectral lines by atoms in a gas dischargetube, and invariance of speed of light, coukl not be understood within tho framework ofclassical physics. To explain these observations a revolutionary framework of explanationwas necessary which we call modem physics. Its two most significant features are relativityand quantum theory. The observations on objects moving very fast, approaching the speedof light, are well explained by the special theory of relativity. Quantum theory has been ableto explain the behaviour of electromagnetic radiation as discrete packets of energy and theparticles on a very small scale are dominated by wave properties.Classical physics is still valid in ordinary processes of everyday life. But to explain thebehaviour of tiny or very fast moving particles, we have to use the above mentionedtheories. In this chapter, we shall discuss Various aspects of theory of relativity and quantum 175

theory. Before introducing special theory of relativity, somerelated terms are discussed briefly.19.1 RELATIVE MOTIONW hen w e say a ball is thrown up. the 'up' direction is only forthat particular place. It will be 'down' position for a person onthe diametrically opposite side of the globe. Th e concept ofdirection is purely relative. Similarly, the rest position or themotion of an object is not same for different observers. Forexample, the walls of the cabin of a moving train arostationary with respect to the passengers sitting inside it butare in motion to a person stationary on the ground. S o wecannot say whether an object is absolutely at rest orabsolutely in motion. All motions are relative to a person orinstrument observing it.Let us perform an experiment m two cars moving withconstant velocities m any direction. Suppose a ball is thrownstraight up. It will come back straight down. Th is will happen inboth cars. But if a person in one car observes the experimentdone in the other car. will he observe the sam e? Suppose nowone car is stationary. Th e person in the other car. which ismoving with constant velocity, throws a ball straight up. H e willreceive the ball straight down. O n the other hand, the fellowsitting in the stationary car obsorves that the path of the ball isa parabola Th us, when experimonters observe what is goingon in their own frame of reference, the same experiment givesidentical observations. But if they look into other frames, theyobserve differently.19.2 FRAM ES O F R E FE R EN C EW e have discussed the most commonly used Cartesiancoordinate system In effect, a frame of referenco is anycoordinate system relative to which measurements are taken.Th e position of a table in a room can be located relative to thewalls of the room. Th e room is then the frame of reference.For measurements taken in the college laboratory, thelaboratory is the reference frame. If the same experiment isperformed in a moving train, the train becomes a frame ofreference. Th e position of a spaceship can be desenbedrelative to the positions of the distant stars. A coordinatesystem based on these stars is then the frame of reference.An inertial frame of reference is defined as a coordinatesystem in which the law of inertia is valid. That is. a body at 176

rest rem ains at rest unless an unbalanced force producesacceleration in it. O th er law s of nature also apply in such asystem . If w e place a body upon Earth it rem ains at restunless an unbalanced force is applied upon it. Th isobservation s h ow s that Earth m a y be considered as aninertial frame of reference. A body placed in a c a r m oving witha uniform velocity with respect to Earth also rem ains at rest,s o that c a r is also an inertial frame of reference. T h u s an yframe of reference which is m oving with uniform velocityrelative to a n inertial frame is also an inertial frame.W h e n the m oving c a r is suddenly stopped, the b o d y placed init. n o lo nger rem ains at rest. S o is the case w h e n the c a r issudd enly accelerated. In such a situation, the car is not aninertial fram e of reference. T h u s an accelerated frame is anon-inertial frame of reference. Earth is rotating andrevolving and hence strictly speaking, the E arth is not aninertial fram e. But it can often be treated as a n inertial framewithout serious error because of very small acceleration.19.3 S P E C IA L T H E O R Y O F R E L A TIV ITYT h e theory o f relativity is concerned with the w a y in which Do You Know?observers w ho are in a state of relative motion desenbephysical phenom ena. T h e special theory of relativity treats -iproblem s involving inertial or non-accelerating fram es ofreference. T h e re is another theory called general theory of Th e K M C or light emm od byrelativity w hich treats problems involving frames of reference fiM hight is c measured b y twoaccelerating with respect to one another. T h e special theory observers, o n s o n f e moWng trackof relativity is based upon two postulates, which can be end the other c«i the rc>»dstated as follows:1 T h e law s of physics are the sa m e in all inertial frames.2. T h e speed of light in free space has the sa m e va lu e for all observers, regardless of their state of motion.T h e first postulate is the generalization of the fact that allphysical law s are the sam e in frames of reference m oving withuniform velocity with respect to one another. If the laws ofphysics w ere different for different observers in relative motion,the observer could determine from this difference that which ofthem were stationary in a space and which w ere moving. Butsuch a distinction does n o t exist, so this postulate implies thatthere is no w a y to detect absolute uniform motion. T h e secondpostulate states an experimental fact that speed of light in freespace is the universal c on stant'd (c = 3 x 10* m s ’). Th e sesimple postulates have far-reaching consequences. These177

include such phenom ena as ihe slowing down of clocks andcontraction of lengths in m oving reference frames asm easured by a stationary observer. S o m e interesting resultsof the special theory of relativity can be summarized asfollows without going into their mathematical derivations.Tim e D ilationA ccording to special theory of relativity, time is not absolutequantity. It de pend s upon the motion of the frame ofreference.S upp o se an observer is stationary m an inertial frame. Hem easures the time interval betw een two events in this frame.Let it be f.. Th is is known as proper time. If the observer ism oving with respect to frame of events with velocity v or if theframe of events is m oving with respect to observer with auniform velocity v, the time m easured by the observer wouldnot be f,. but itw ould be t given by (1 9 .1 ) one. so t is greaterthan (.i.e ., time has dilated or stretched due to relative motionof the observer and the frame of reference of events. Thisastonishing result applies to all timing processes - - physical,chemical and biological. Even aging process of the humanbody is slow ed by motion at very high speeds.Le n gth C o n tra ctio nT h e distance from Earth to a star m ea sured by an observer ina m oving spaceship would seem smaller than the distancem easured b y a n observer o n Earth. Th a t is. if you are inmotion relative to two points that are a fixed distance apart,the distance between the tw o points appears shorter than ifyou were at rest relative to them. Th is effect is known aslength contraction. Th e length contraction happens onlyalong the direction of motion. N o such contraction would beobserved perpendicular to the directign of motion. Th e lengthof an object or distance between two points measured by anobserver w h o is relatively at rest is called proper length Ifan object a n d an observer are in relative motion with speed v.then the contracted length 'C is given by 178

(192)M ass VariationAccording to special theory of retativity, mass of an object is avarying quantity and depends upon the speed of the object.An object whose mass when measured at rest is m0will havean increased mass m when observed to be moving at speedv. They are related by ' V ........ (193>Th e increase in mass indicates the increase in inertia theobject has at high speeds. As v approaches c. it requires alarger and larger force to change the speed of the object.As v—>c, — —> 1 therefore , T - - y -» 0 c ic*Thus mAn infinite mass would require an infinite force to accelerateit. Because infinite forces are not available, hence, an objectcannot be accelerated to the speed of light '<?in free space.In our everyday life, we deal with extremely small speeds,compared to the speed of light. Even the Earth's orbital speedis only 30 k m s O n the other hand, the speed of light in freespace is 300.000 kms ’. This is the reason why Newton's lawsare valid in everyday situations. However, whenexperimenting with atomic particles moving with velocitiesapproaching speed of light, the relativistic effects are veryprominent, and experimental results cannot be explainedwithout taking Einstein's equations into account.E n e rg y - Mass RelationAccording to special theory of relativity, mass and energy aredifferent entities but are interconvertible. Th e total energy £and mass m of an object are related by the expression £ =mc’ (19.4)where m depends on the speed of the object. At rest, theenergy equivalent of an object's mass m, is called rest massenergy £„. 179

E .= m ,< ? ............. (19.5)As me* is greater than mtc\ the difference of energy(me?- mjc?)is due to motion, as such it represents the kineticenergy ofthe mass. HenceK.E. = (m - m 0) c 2 ............. ( 19.6 )From equation 19.4 above, the change in mass m due tochange in energy A£ is given byBecause o' is a very large quantity, this implies that smallchanges in mass require very large changes in energy. In oureveryday world, energy changes are too small to providemeasurable mass changes. However, energy and masschanges in nuclear reactions are found to be exactly inaccordance with the above mentioned equations.N A V STA R Navigation SystemTh e results of special theory of relativity are put to practicaluse even in everyday life by a modem system of navigationsatellites called N A V STA R . Th e location and speedanywhere on Earth can now be determined to an accuracy ofabout 2 c m s ’. However, if relativity effects arc not takon intoaccount, speed could not be determined any closer thanabout 20 cms ’. Using these results the location of an aircraftafter an hour's flight can be predicted to about 50 m ascompared to about 760 m determined by without usingrelativistic effects.E x a m p le 19.1: Th e period of a pendulum is measured to be3.0 s in the inertial reference frame of the pendulum. What isits period measured by an observer moving at a speed of0.95 c with respect to the pendulum?S o lu tio n :

E x a m p le 1 9 .2 : A bar 1.0 m in length and located alongx-axis moves with a speed of 0.75 c with respect to astationary observer. W hat is the length of the bar asmeasured by the stationary observer?S o lu tio n : fo= 1 .0 m , v = 0 .7 5 c . £ = ?Using ( r: f 0| l - ^ 1r = 1.0m x 1.001X^1-(0 .7 5 )1 - 0.66 mE x a m p le 1 9 .3 : Find the mass m of a moving object withspeed 0.8 c.S o lu tio n :Usingor m : 1.67 m„or m = 1.67 m0 (• Absorption o ( radabon F i g 19.119.4 B LA C K B O D Y RADIATIONWhen a body is heated, it emits radiation. Th e nature ofradiation depends upon the temperature. At low temperature, abody emits radiation which is principally of long wavelengths inthe invisible infrared region. At high temperature, the proportionof shorter wavelength radiation increases. Furthermore, theamount of emitted radiation is different for differentwavelengths. It is of interest to see how the energy is distributedamong different wavelengths at various temperatures. Forexample, when platinum wire is heated, it appears dulf red atabout 500 °C. changes to cherry red at 900:C . becomes orangered at 1100°C. yellow at 1300:C and finaty white at about1600=0. This shows that as the temperature is increased, theradiation becomes richer in shorter wavelengths.In order to understand the distribution of radiation emitted froma hot body, we consider a non-reflecting object such as a solid I8I

*mo» that has a hollow cavity within it. It has a sm all hole and the hoi* radiation can enter or escape only through this hole. Th e inside is blackened with soot to m ake it a s good a n absorber(b| Em auoo of rad<*bon and as bad a reflector as possible. Th e small hole appears F ig . 19.1 black because the radiation that enters is reflected from the inside w alls m any times a n d is partly abso rb ed at each For Your Information reflection until none rem ains. S u c h a body is term ed as black body and has the property to absorb all the radiation entering it. A black body is both an ideal absorber (F ig . 19.1 a )a n d a n ideal radiator(F»g. 19.1 b). Inte nsity D istrib ution D iagram Lum m er and Pringsheim measured the intensity of emitted energy with w avelength radiated from a black body at different temperatures by the apparatus shown in F ig .19.2. T h e am ount of radiation emitted with different w avelengths is show n in the form of energy distribution curves for each temperaturo in the Fig. 19.3. black body cavity rock tax pnsm (tranvntt and daperse* ai wavelengths) F I* 1*2 Th e s e curves reveal the following interesting facts. A t a g iven temperature, the en ergy is not uniformly distributed in the radiation spectrum of the body. 2 . At a given temperature T, the emitted energy has maximum value for a certain wavelength and theF ig 19 3 R m uC s o f Lum m er and product / v . x f remains constant. .............. (1 9 .7 )Pn n gshem ’s eipenm enl* graphs of > _ x T = Constantrnleowty oI redated energy a g e n t!wavelength Irom a btackbody T h e value of the constant known a s W ie n 's constant is about 2 .9 x 10'* m K. Th is equation m ea ns that as T 182

increases. X _ . shifts to shorter w avelength.3. For all wavelengths, an increase in temperature causes an increase in energy emission. Th e radefcm intensity increases with increase in wavelengths and at aparticular wavelength , it has a maximum value. Withfurther increase in wavelength, tho intensity decreases.4 T h e area under each curve represents the total energy ( £ ) radiated per second per square metre o v e r all w avelengths at a particular temperature. It is found that area is directly proportional to the fourth pow er of ketvin temperature T . Th u s£ x T* or £ =<j t ‘ (19.8)w here o is called Stefen's constant. Its value is 5 .6 7 x 10\"*W m 'IC * a n d the a b o ve relation is know n a s Stefen-B oltzm ann law.P la n c k ’s A s s u m p t io nElectrom agnetic w a v e theory of radiation cannot explain theenergy distribution along the intensity-wavelengths curves.Th e successful attempts to explain the shape of energyd is trib u tio n c u rv e s g a v e rise to a ne w andnon-classical view of electromagnetic radiation. In 1900. MaxPlanck founded a mathematical model resulting in anequation that describes the shape of observed curvesexactly. H o suggested that e n e rg y is radiated or absorb ed indiscrete packets, called quanta rather than as a continuousw ave. E a ch quantum is associated with radiation of a singlefrequency. T h e en ergy £ o f each quantum is proportional toits frequency/.and £=h/ (1 9 .9 )w here h is Planck's constant. Its value is 6.6 3 x 10'* J s . Th isfundamental constant is a s important in physics as theconstant c. the speod of light in vacuum.M ax P lanck received tho N ob el P rize in physics in 1918 forhis discovery of energy quanta.Th e PhotonPfanck suggested that as matter is not continuous butconsists of a large num ber o f tiny particles, s o is the radiationen ergy from a sourco. H e assum e d that granular nature of 183

radiation from hot bodies was due to some property of theatoms producing it. Einstein extended his idea andpostulated that packets or tiny bundles of energy are integralpart of all electromagnetic radiation and that they could notbe subdivided. These indivisible tiny bundles of energy hecalled photons. The beam of light with wavelength >. consistsof stream of photons travelling at speed c and carries energyhf. From the theory of relativity momentum p of the photon isrelated to energy as E=pc ............. (19.10)Thus pc = hf or P ^ — = - ............. (19.11) CAThe table 19.1 relates the quanta emitted in different regionsof the electromagnetic spectrum with energy. At the high end.y- radiation with energy - 1 MeV is easily detected as quantaby a radiation detector and counter. At the other end. theenergy of photon of radio waves is only about 10\" 5eV. Somillions of photons are needed to detect a signal and hencewave properties of radio waves predominate. The quanta areTable: 19.1 Electrom agnetic spectrumImfwiY, 11/ -184

so close together in energy value that radio waves aredetected as continuous radiation.Th e emission or absorption of energy in steps may beextended to include any system such as a mass oscillating ona spring. However, the energy steps are far too small to bedetected and so any granular nature is invisible. Quantumeffects are only important when observing atomic sizedobjects, where h is a significant factor in any detectableenergy change.E x a m p le 19.4: Assuming you radiate as does a blackbodyat your body temperature about 37 °C, atwhat wavelength doyou emit the most energy?Solution: T 37°C = 310K W ien's constant = 2.9xlO ~5 mK Using ^ x T Constant ’ ^ o k \" * ' 9 35 * 1cr' m ■9 35The radiation lies in the invisible infrared region and isindependent of skin colour.E x a m p le 19.5: What is the energy of a photon inabeam ofinfrared radiation of wavelength 1240 nm?Solution: X = 1240 nm . E =?Using E ■ hf ^or A E = 6.63xl0>«Jsx3x10»m s_-: = 1 6x1 0, t j 1240x10 8 m E - 1.0 eV19.5 IN T E R A C T IO N O F E L E C T R O M A G N E T IC R A D IA TIO N W ITH M A TTE RElectromagnetic radiation or photons interact with matter inthree distinct ways depending mainly on their energy. Thethree processes are 185

(i) Photoelectric effect (ii) C om pton effect (in) Pair production P ho toelectric Effect T h e emission of electrons from a metal surface when exposed to light of suitable frequency is called the photoelectric effect. T h e emitted electrons are known as photoelectrons.f i g 1 * 4 Experimental arrangemerU T h e photoelectnc effect is demonstrated b y the apparatusto cfcaerre e * »* > o t«tn c eWect shown in Fig. 19.4. A n evacuated glass tube X contains two electrodes. T h e electrode A connected to the positivePHotoelectrc I, >/. terminal of the battery is known a s anode. T h e electrode C current connected to negative terminal is known as cathode. W h e nJi ♦ v -» m onochrom atic light is allow ed to shine on cathode, it begins to emit electrons. T h e s e photoelectrons are attracted by the < _ -v positive anode and the resulting current is m easured by an amm eter. T h e current stops w h e n light is cut off. w hichF ig 19.5 CM recteratic c u v e t otptiotocurrenl v*. a (f* e d voltage lor proves, that the current flows because of incident light. Th istwo mtensAes ot mooocf-romou: current is. henco. called photoelectric current. T h e m axim umIghC energy of the photoelectrons can be determined by reversing the connection of the battery in the circuit i.e.. n o w the anode A is negative and cathode C is at positive potential. In this condition the photoelectrons are repelled by the anode and the photoelectric current decreases. If this potential is m ade m ore and more negative, at a certain value, called stopping potential V0, the current be com es zero. E v e n the electrons of m axim um energy are not able to reach collector plate. Th e m axim um en ergy of photoelectrons is thus -1m v 2' (19.11) 2*<— -V o ♦V — > w here m is m ass, v is velocity and e is the ch a rge on electron. If the experiment is repeated with light beam of higherF ig 1 9 4 C tw e c te rW c curve* otptiotocurrent v*. appt* 0 votog* for intensity, the am ount of current increases but the currenttgh»c^<Ht*rentfr*qu«oer*» stops for the sam o value of V,. T h e F ig .19.5 show s two curvos of photoelectric current as a function of potential V w here / ,> / ,. If. how ever, the intensity is kept constant and experim ent is perform ed with different frequencies of incident light, w e obtain the curve s show n in F ig .19.6. T h e current is sam e but stopping potential is different for each frequency of incident light, w hich indicates the proportionality of m axim um kinetic e n e rg y with frequency of light t. 18 6

The important results of the experiments are For Your Information1. Th e electrons are emitted with different energies. Th e maximum energy of photooloctrons depends on the particular metal surface and the frequency of incident light.2. There is a minimum frequency below which no electrons tare emitted, however intense the light may be. Thisthreshold frequency/, varies from metaltometal. *£_Electrons are emittod instantaneously, the intensity oflight determines only their number.These results could not be explained on the basis of A graph oI the marimum Unetcelectromagnetic w ave theory of light. According to this energy o l photoetoctrone v* *gMtheory, increasing the intensity of incident light should frequency. Below a certainincrease the K .E . of emitted electrons which contradicts theexperimental result. Th e classical theory cannot also explain ^ ^ ocy- ^the threshold frequency of light.Explanation on the Basis of Quantum TheoryEinstein extended the idea of quantization of energyproposed by Max Ptanck that light is emitted or absorbed inquanta, known as photons. Th e energy of each photon offrequency /as given by quantum theory is E=hfA photon could be absorbed by a single electron in the metalsurface. T h e electron needs a certain minimum energy calledthe work function ’O ' to escape from the metal surface. If theenergy of incident photon is sufficient, the electron is ejectedinstantaneously from the metal surface. A part of the photonenergy (work function) is used by the electron to break awayfrom the metal and the rest appears as the kinetic energy ofthe electron. That is.InckJont photon energy - Work function = Max K E . d photoelectronor h/- <t> = - m v,L (19.12) 2Th is is known as Einstein's photoelectric equation.W hen K . E ^ of the photoelectron is zero, the frequency / isequal to threshold frequency /* hence the Eq. 19.12 becomesh/.-0> = 0 or 0 = h/. (19.13)Hence, w e can also write Einstein's photoelectric equation as 187

K£*m> « h f - h f 0 .............. (1 9 .1 4 )q u artz O f g lM * tub* It is to b e noted that all the emitted electrons d o not possess catfvxl* the m axim um kinetic energy, som e electrons co m e straight out of the metal surface and som e lose energy in atomic collisions before coming out. Th e equation 19.14 hoWs good on ly for those electrons w hich com e out with full surplus energy. Albert Einstein w a s aw arded Nobel P rize in physics in 1921 for his explanation of photoelectric effect. Note that the phenom enon of photoelectric effect cannot be explained if w e a ssum e that light consists of w a ve s and en ergy is uniformly distributed over its wavefront. It c a n only be explained b y assum ing light consists of corpuscles of en ergy know n as photon. T h u s it s h ow s tho corpuscular nature of light. Photocellr >g 1 * .: S « T * o p to to -o m M s ftQ c o l A photocell is based o n photoelectric effect. A simple photocell is show n in Fig. 19.7. It consists of an evacuated («) glass bulb with a thin anode rod and a cathode of an appropriate metal surface. T h e material of the cathode isfig 1 9 * S o u ndIra c*o n• ttn«N c# > selected to suit to the frequency range of inddent radiationvan** Vi* ini«n**y of Ig h t rM cM n gV * photo O H . o v e r w hich the cell is operated. For oxam ple sodium or potassium cathode emits electrons for visible light, cesium coated oxidized silver emits electrons for infrared light and so m e other metals respond to ultraviolet radiation. W hen photo-em issive surface is exposed to appropriate light (F ig .19.8 a ), electrons are emitted and a current flows in the external drcuit which increases with the increase in light intensity. T h e current stops w hen the light beam is interrupted. T h e cell has wide range of applications. S o m e of these are to operate:bjh< 1. Security system s :: 2. Counting systems 3. Automatic door systems sound tr> ^ 4 Autom atic street lighting 5. Exposure meter for photography (b )F*V 1 9 .8 P r o t o c o l <J*toetton o rc u * Sound track of movies (Fig.19.8 b)ftx s ou nd * » c * of moYio* E x a m p le 1 9 .6 : A sodium surface is illuminated with light of w avelength 300 nm . T h e work function of sodium metal

is 2.46 eV.(a ) Find the maximum K .E . of the ejected electron.(b ) Determine the cut off wavelength for sodium.Solution: X = 300nm. 0 = 2.46eV Ka(a ) Energy of incident photon E = hf = —or E = 300x10 m = 6.63 x 10 19 J £ = 4.14oVN ow K .E mn = h f -C > 4 .1 4 e V - 2 .4 6 e V = 1.6 8 eV(b ) <t>= 2.46 e V = 3.94 x 10 **JUsing <J>= h/0 = ^ 0or ?.o = tl£ = 6 . 6 3 x 1 0 - » J s x 3 x l 0 » m s - = 5 0 5 x 1 0 ?m0 <t> 3.94x10 ” J X0 • 505 nmTh o cut off wavelength is in the green region of the visiblespectrumC o m p to n Effect (•)Arthur Holly Compton at Washington University in 1923 F>g.l9.9 ( « ) Corr^lon'% *c*t1onngstudied the scattering of X -rays by loosely bound electronsfrom a graphite target (Fig. 19.9 a). H o measured the OJHJ*nr>*rtwavelength of X -rays scattered at an angel 0 with the originaldirection. He found that wavelength X, of the scattered X-raysis larger than the wavelength X of the incident X-rays. Th is isknown as Compton effect. Th e increase in wavelength ofscattered X-rays could not be explained on the basis ofclassical w ave theory. Compton suggested that X-raysconsist of photons and in the process of scattering thephotons suffor collision with electrons like billiard balls(F ig .19.9 b & c). In this collision, a part of incident photonenergy and momentum is transferred to an electron. Applyingenergy and mom entum conservation laws to the process, hederived an expression for the change in wavelength AXknown as Compton shift for scattering angle 0 as 189

AX = (1 -C O S O ) (19.15)A -IV X , f t 0 9 otoctron where m . is the rest mass of the electron Th e factor — h has m ec E dimensions of length and is called Compton wavelength and has the numorical value h 6.63 x 10 ^ Js 2.43x10''* m m0c 9.1x10 51k g x 3 x 1 0 * m s 1 If the scattered X -ray photons are observed at 0 = 90°. the Compton shift AX equals the Compton wavelength. Th e E q .19.15 was found to be in complete agreement with Compton's experimental result, which again is a striking confirmation of particle like interaction of electromagnetic waves with matter. Arthur Holly Compton was awarded Nobel Prize in physics in 1927 for his discovery of the effect named after him. («) E x a m p le 19.7: A 50 keV photon is Compton scattered by a quasi-free electron. If the scattered photon comes off at 45°.F »g 19.9 (t> )A p tw X o n c o M o * w W ia o what is itswavelength?• i»ctrenand(c)8o9 iar**c«nor«<3 Solution: E - 50 k e V = 5 0 x 103 x 1 . 6 x 1 0 19 J Using m „T or X -h-e 6 .6 3 x 1 0 ^ Js x 3 x 1 0 * ms 1 = 0.0248 nm 50x10* x 1 .6 x 1 0 ',# J Now X’ - / . - —me (1 -C O S 4 5 0) X '-X - 6 .6 3 x 1 0 ** Js - j (1-0.707) 9.1x10 J ,k g x 3 x l0 * m s = 0.2429 x 1 0 \"m x 0 .2 9 3 X '- X i 0.0007nm X '- x - f 0.0007 nm X' = 0.0248 nm + 0.0007 nm = 0.0255 nm 190

Pair Production photon IIn the previous sections you have studied that a low energyphoton interacting with a metal is usually completely Vabsorbed with the emission of electron (Photoelectric effect)and a high energy photon such as that of X-rays is scattered P tx Productionby an atomic electron transferring a part of its energy to the F ig . 19.10electron (Compton effect). A third kind of interaction of veryhigh energy photon such as that of y-rays with matter is pairproduction in which photon energy is changed into anelectron-positron pair. A positron is a particle haying mass andcharge equal to that of electron but the charge being ofopposite nature i.e. positive. The creation oftwo partides withequal and opposite charges is essential for chargeconservation in the universe. The positron is also known asantiparticle of electron or anti-electron. The interactionusually takes place in the electric field in the vicinity ofa heavynucleus as shown intheFig.19.10so that there is a particle totake up recoil energy and momentum is conserved.In the process, radiant energy is converted into matter inaccordance with Einstein's equation E - me', and hence, isalso known as materialization of energy. For an electron orpositron, the rest mass energy = m.C1= 0.51 MeV. Thus tocreate the two particles 2 x 0.51 MeV or 1.02 MeV energy isrequired. For photons of energy greater than 1.02 MeV. theprobability of pair production occurrence increases as theenergy increases and the surplus energy is carried off by thetwo particles in the form of kinetic energy. The process can berepresented by the equationEnergy of photon 1jK ln e U c energy 1 [for pair production ! |of the partides !hf = 2m0c2 + K.E. (e ) + K.E. ( e ') ............ (19.16)19.6 A N N IH IL A T IO N O F M A T T E RItis converse of pair production when a positron comes closeto an eledron they annihilate or destroy each other. Thematter of two particles changes into electromagnetic energyprodudng two photons in the y-rays range. e »y + yThe two photons are produced travelling in oppositedirections (Fig. 19.11) so that momentum is conserved. Each 191

y.phoioo photon has energy 0.51 MeV equivalent to rest mass energy ofa particle. * The existence of positron was predicted by Dirac in 1928 and T it was discovered in the cosmic radiation in 1932 by Carl Anderson. It gradually became dear that every partide has aFtg. 19.11 corresponding antiparticle with the same mass and charge (if it is a charged partide) but of opposite sign. Partides and antiparticles also differ in the signs of other quantum numbers that we have not yet discussed. A particle and its antipartide cannot exist together at one place. Whenever they meet, they annihilate each other. That is. the partides disappear, their combined rest energies appear in other forms. Proton and antiproton annihilation has also been observed at Lawrence Berkeley Laboratory. 19.7 WAVE NATURE OF PARTICLES It has been observed that light displays a dual nature, it acts as a wave and it acts as a partide. Assuming symmetry in nature, the French physicist, Louis de Broglie proposed in 1924 that partides should also possess wavelike properties. As momentum p of photon is given by equation 19.11. h P =I de Broglie suggested that momentum of a material partide of mass m moving with velocity v should be given by the same expression. Thus p = -h * m v or x « p- = —m v ............. ( 19.17) Do You Know? where X is the wavelength associated with partide waves. Hence an electron can be considered to be a partide and itLight a . « short, th* m o st refined can also be considered to be a wave. The equation 19.17 ist o r n o t m e tie r ( L o u * d o Brogfco called de Broglie relation.1892-1987) An object of large mass and ordinary speed has such a small wavelength that its wave effects such as interference and diffraction are negligible. For example, a rifle bullet of mass 20 g and flying with speed 330 m s ' will have a wavelengthX given by X ■ — . — f f f f i - 1. ? . - - ,1 * 1 0 * m mv 2x10 7kg*330ms 192

T h is w avelength is so small that it is not m easurable ordetectable by a n y of its effects.O n the other hand for an electron m oving with a speed of1 x 10‘ m s ',T h is w avelength is in the X -ra y s range. T h u s , diffractioneffects for elebtfifchs ate m easurable w hereas diffraction orinterference effects for bullets are not.A cdrivinclng G w e n t e Qf the w ave nature of electrons was 'provided b y CtiHfdi^J. Davissdn and Laster H. Germ or. Th e y cs h o w e d th atlele ctto nsiw e diffractod from: metal crystals in r i g . 19.12 Eipertm enW errenaem ertexactly the same manrtor as X-rays or any other w ave. Th e o'0avo*or> end G e rm * lor electronapparatus u s p d 'b y thorn is s h ow n in Fig. 19.12. in which tfttectonelectrons, /rom heated filament are accelerated by anadjustable applied voltage V. T h e electron beam of energyVo is m ade incident on a nickel crystal. T h e beam diffractedfrom crystal surface enters a detector and is recorded as acurrent /. T h e gam in K .E . of the electron as it is acceleratedb y apo ten tial V in the electron g u n isg iv e n b y 1 = v®or ; m v = -j2 m V eFrom de Broglie equationThus (1 9 .1 8 )In one of the expenments. the accelerating voltage V w a s 54volts, hence I.W 9' **rTH ls feiJam of electrons diffracted from crystal Surface w asobiarifed for a glancirig'tfngle o f 65°. A ccording to Bragg's,

equation 2 d s in 0 = m>. F o f 1st order diffraction m = 1 For nickel d = 0 .9 1 x 1 0 ''* m Thus 2 x 0.91 x 10\"10 m x sin 65® ■ >. w hich gives Ji= 1 .6 5 x 1 O’* mFoi Your Inloim.ition Th u s , experimentally observed w avelength is in excellent agreem ent with theoretically predicted wavelength.8*»mc# Diffraction patterns have also been observed with protons,•4*e*oos neutrons, hydrogen atoms and helium atoms thereby giving substantial eviden ce for the w ave nature of particles. (*»> For his work on the dual nature of partides. Prince Louis(• ) It •'♦■aro-n W h a i M as c-scr* * Victor de Broglie received the 1929 Nobel Prize in physics.par.c** w in no wave pvopeme*. Clinton Joseph Davisson and G eorge Paget Thom sonItiey * o t t t pas* through e ve or the shared the Nobel Prize in 1937 for their experimentalOther d the two tM s and tttk e the confifmatton of the w ave nature of partides.screen caus-rg « to g b w andr e d u c e e > a o m ag e * of the u t s (b ) W ave P article D ua lity•n reewy the screen revest* a patternof t n j r t w i dark h n g e * simaar to Interference and diffraction of light confirm its w a v e nature, while photoelectric effect proves the partide nature of light. a used and *it#r«er»«ce occurs Similarly, the experiments of Davisson and G erm er andbetween the »ght wave* oowsng from G P. T h o m s o n reveal w a v e like nature of electrons and in thee a c h iM experiment of J . J . Th o m so n to find e/m w e had to assume partide like nature of the electron. In the sam e w a y w e are forced to a s s u m e both wavelike a n d particle like properties for all matter: electrons, protons, neutrons, molecules etc. and also light, X -ra y s , y-rays etc. have to be included in this. In other w ords, matter and radiation have a dual ‘w a ve - partode’ nature and this n e w concept is know n as w ave partide duality. Niels Bohr pointed out in stating his principle of complementarity that both w ave and partide aspects are rsquired for the complete description of both radiation and matter. Both aspects are always present and either m ay be revealed by an experiment. However, both aspects cannot be revealed simultaneously in a single experiment, which aspect is revealed is determ ined by the nature of the experim ent being done. If you put a diffraction grating in the path o f a light be am , you reveal it as a w ave. If you allow the light beam to hit a metal surface, you need to regard the beam as a stream of partides to explain your observations. T h e re is n o sim ple experim ent that you can carry out with the 194

beam that will require you to interpret it as a wave and as apartide at the same time. Light behaves as a stream ofphotons when it interacts with matter and behaves as a wavein traveling from a source to the place where it is detected. Ineffect, all micro-particles (electrons, protons, photons, atomsetc.) propagate as if they wero waves and exchange energiesas ifthey were particles - that is the wave particle duality.E xam ple 19.8: A particle of mass 5.0 mg moves with speedof8.0 ms\". Calculate itsde Broglie wavelength.Solution: m = 5.0 mg = 5.0 x 10'* kg v * 8.0 ms\" h = 6.63x10 JsUsing x „ J L ^ x IO ^ 66x1Q.Wmme 5.0*10 * kg x 8.0 msE xam ple 19.9: An electron is accelerated through aPotential Difference of 50 V. Calculate its de Brogliewavelength.Solution: V# = 5 0 V . m - 9.1 x 10-* kg.X -? . • ■ 1.6x10\"\" Cthen ^ 2 x 9.1 x 10'3'k g x 50 J C ’ x 1 .6 x 1 0 -\" C . 1.74x10'\" mUses of Wave Nature of ParticlesThe fact that energetic particles have extremely shortde Broglie wavelengths has been put to practical use in manyultra-modem devices of immense importance such aselectron microscope. 195

E le c t r o n M ic r o s c o p e q ie lm oJ iyO< 9 iiu p 0 i lliw JsrtJ met# tfectfcn n&tSfElectron •ncrosocpo ( Block D iagram Irani3whidh’ ©ffab^jsYv? F ig . 19.13 dolills nof w s$le vyyi bj mlcroscop# $ecW c aWefi Oo You Know? lenses are u3e<f(,tbV ftfIn the subalomc wortd lew thngt can Q^pmagneUi?>forjieettKM,<K^ v erted ,o n m etft^otprgec.b c p iu O cM O vW M O O % p r»ca on The resulting o o < | o o ^ ,o t ^ e « p ^ r o n » b e « m « d r e «ni9ar to the refraction effects produced by glass lenses used to focus light in optical microscope. The e:ecf&fWulfi& accelerated to highepergi^s by applying voltage from 30 kV to soverai megavotts. i>uch lugh voltages give extremely short wavelength and also givo the electron sufficient energy to penetrate specimen of reasonably thickness. A resolution of 0.5 tc 1 nm is possible'with a 50 kV microscope as co^pfi.^1 to^yst optkSil re&*utfoMf 0.2 pm. A schematic diagram of me electron;rulcrp3cope is ;shown in the Figure 1?. 13. The magnetic conducting lens concentrates the beam the specimen? ebcfrtMS W stti*e #d-«tit?bf W ’&bem from ttfe m*Sk«rr’p a W e6r the' specimen. Th e transmitted beam theroforo hb£lit&t?al differences in density that correspond to the feature specimen. Tq e ppjecfcve and intermediate,lenses produce a real intermedtetr image and preaction lens forms the final image which csn b§ vigyfecf)On 3 fluorescent screen or photographed on special film known as electron micrograph. A three dimensional image of rcmaj^bJe.auatity can be achiavod by modem versions called ‘ scanning electron 19.8 UNCERTAINTY PRINCIPLE , - - I .\ nod! Position and momentum of aegdrtidq cannot both be measured simultaneously with perfect accuracy. There is always a fundarheniaH uncSrarnty assocuiled with any meayprfeipeota This gowrtafnly'i® not associated with tf*e measuring instrument. It is a consequence of the wave particle duality of matter and r&diafion. This was first proposed by Werner Heisenberg in 1527 and hence ts Known as Heisenberg Uncertainty Pnnciple. This fundamental unodrtalrrty'ls-'coi.ipweiy^WagiigibiadformeaiuiteiTlehls ofr position and momentum o fw a c / o s tc ^ c objects but is a predominant fact of life in the atomid domain. For example, a stream of light photons scattering from a flying1teflrilSbells IW»|

hardfy affects its path, but one photon sinking an electrondrastically alters the electron's mpjiofl, Since light has gisowave properties, we would expect tobe able to determine theposition of the electron only to within one wavelength of thelight being used. Rend#. Htwder toobserve the positionelectron with less uncertainty and also for minimizirdiffftttfd* I s f e 'J W 'r t O K i M i f f \" .........................will alter P m m M S i m 9 ^ » le»HB8fte'8toP b rem e ntis ?emiJairti A x »XAt most, the photon of light can transfer all its momen/um 9lgbnhq yfnisheonu gnieuI - | to the micro particle whose ofwn^rv^pentum will then beuncertain by an artfoufcPr •20. f rf ^ 0*.x20.r = 3A : rr.e r 0lqmsx3to beeqe eitl bluow ferlW .(m V ftrix O .r ) euetoun ®d» to e jje Ax^ftJiW^>b&wewh'K-edThe equation 19.19 is the mathematical form of cM8M^yftf9 For Your InformationM W H to H slatesV m the p ra M o H ty M A M riito t^ho**uto You can n a v w accurately d o tc rb a Mlpi^fWtapartjcfflcats.yneinetaittflMKiitoeiuaoerWrhB VtleIhe-.ix-soojpoeeniKpfofts. rsom^rttwe/ abrthensafrmsM*!**# cccoaspects of a subafeyric parttcto atapproximately equals Plancfc^CJXWfthttehoonu giedneeleHTh e re is another form of u n £ e r j^ t y principlo which relatesthe e n e rgy of a particle a n d the time at w hich it h ad theenergy. If the A £ is the uncertainty in o u r know ledge of theenergy of our particle and ifjjjetiH&IViterval during w hich to A£ ATthe particle l « d the e n e r g y ^ f - ^ r then rf JSSfr:.A/*n w o rtto rit energy. auetounAccording to Heisenberg’s more careful calculations, hefound that at the very best

A X .A p ih (19.21)and A f.A f 2 h (19.22)where h = 1 .0 5 x 1 0 MJsW em e r Karl Heisenberg received Nobel Prize for physics in1932 for the development of quantum mechanics.E x a m p le 1 9 .1 0 : T h e life time of an electron in an excitedstate is about 10* s. W hat is its uncertainty in energy duringthis time?S olution:Using uncertainty principle A E.A t« h ^ h 1.05x10 * Js Af 10 8 s A E = 1.05x10'w JE x a m p le 19 .1 1 : A n electron is to be confined to a box of thesize of the nucleus (1.0 x 1 0 Mm ). W hat would the speed ofthe electron be ifit were so confined?S olution:Maximum uncertainty In the location of electron equals thesize of the box Itself that Is Ax = 1.0 x 10 Mm . Th e minimumuncertainty in the velocity of electron is found fromHeisenberg uncertainty principle Ap m— AXor m A v . AAv, h . . f f ” 10* * -1 .1 5 x 1 0 -n .a -mAx 9.1x10 kgx1.0x10 mFor confinement In the box. the speed should be greater thanthe speed of light. Because this is not possible, w e mustconclude that an electron can never be found inside thenucleus. 19 8

esm av• An inertial frame of reforonce is defined as a coordinate system in which the law of inertia is valid. A frame of reference that is not accelerating is an inertial frame of reference.• The special theory of relatively treats problems involving inertial or non-accelerating frames ofreference. Itis based upon two postulates.(i) The laws ofphysics are the same inall inertial frames. „\ .(ii) The speed of light in free space has the same value for all observers, regardless of their state of motion.• E = m c is an .mportant resultof special theoryof relativity• A black body is a solid block having a hollow cavity within it. It has small hole and the *radiation can enter or escape only through this hole.• Stephen Boltzmann law states that total energy radiated over all wave length at a •particular temperature is directly proportional to the fourth power of that Kelvintemperaturo.• Tho emission of electrons from a metal surface when exposed to ultraviolet light iscalled photoelectric effect. The emitted electrons are known as photoelectrons.• When X-rays are scattered by loosely bound electrons from a graphite target, itknown as Compton effect. «•• The change of very high energy photon into an electron, positron pair is called pairproduction.• When a positron comes dose to an electron, they annihilate and produce twa•photons inthe y - rays range. Itis called annihilation of matter.• Position and momentum of a partide cannot both be measured simultaneously with perfect accuracy. There is always a fundamental uncertainty assodated with any measurement. It Is a consequence of the wave partide duality of matter and radiation. Itis known as Heisenberg uncertainty principle. g ese®19.1 what are the measurements on which two observers in relative motion will always agree upon?19.2 Does the dilation means that lime really passes more slowly in moving system or that itonly seems to pass more slowly?19.3 ifyou are moving in a spaceship at a very high speed relative to the Earth, would you noticea difference (a) in your pulse rate (b) in the pulse rate of people on Earth? 199