Phys-Chem Accelerated Research Project

PHYSICS-CHEMISTRY ACCELERATED COLLABORATIVE RESEARCH PROJECT QTHUEAONRTYUM Prepared for: Ms.Patraphorn Sanguansat Mr. Gopinath Subramanian Accelerated Chemistry & Physics Grade 11 Section 1 Quarter 3 Year 2021 Mahidol University International Demonstration School

Table of Contents 01 Introduction 02 Quantum Theory 03 History of Quantum Theory 04 Planck's Constant 05 Electromagnetic Waves 06 Classical Theory VS Modern Theory 07 Spectrum & Bohr's Model QUANTUM REPORT 2021 01

08 Photoelectric Effect 09 Spectroscopy: Interaction of Light & Matter 10 Feynman Diagram 11 Applications 12 Citation QUANTUM REPORT 2021 02

Introduction Einstein once said “God does not play dice (his words), he only plays mahjong (not Einstein’s words).” In order to be able to perceive the wise words, we need to first understand the concept of Mahjong. Mahjong is a Chinese tile based game that has rules governing them, much like how it is in the going-ons of the universe. In Mahjong , they usually need the presence of 4, typically old ladies with skills including but not limited to tactics, observation, memory, and adaptive strategy. Where do these ladies come from? They are from the lawful community where everything is occurring due to laws. Nothing is randomly done. Events happened in respect to the principles of the universe. Therefore, Some may say that, “Humans are the accident of God.” Now, with wit, humans should come to realize that this is totally a lie. No one is created due to chance, there are laws and reasons behind our existence. And what allows these ladies to be able to play Mahjong with their fullest potential; the answer is the numerous number of intelligent brain cells. Cells are the building blocks of life, but what are the cells made from? 03

Poof! Unlike the magic shows that we watch in our childhood, humans don’t simply appear from a top hat out of nowhere like rabbits. Cells that make up living things came from prokaryotic beings that merged with each other, some billions years ago. During a time before multicellular creatures exist, Early Earth, if you will, there were only simple cells. Those cells are synthesized abiotically into organic molecules, and those molecules join together into macromolecules which are packaged into protocells. Eventually, self replicating molecules form, and a plethora of single celled organisms was born. And then, multicellular organisms were born, from these single celled organisms becoming one, creating these ladies who play mahjong. But of course, while human beings and other living beings are built upon using these building blocks, cells, inanimate objects are built from an even smaller particle, called atoms. Before we could introduce the concept of atom and the theories that proceeded after the discovery of atoms. We must address the pre-atomic era, when humans had not yet brought atoms into the spotlight. Let’s call this a “Pre-pre-atomic era” because what we are going to light our interest in is the period before enlightenment starting from the Iron age. 04

The concept that anything can be broken down into smaller, indivisible components called atoms is 2,250 years older than the discovery of the atom. It was sometime in the 5th century when a Greek philosopher called Leucippus proposed the theory that all matter is made up of extraordinarily small, indivisible particles. His philosophy became known as atomism, and he called them atoms. Leucippus' theories were elaborated upon by other Greek thinkers. Furthermore, atomism emerged in other parts of the ancient world, such as India, where Buddhist philosophers developed their own theories after learning about Leucippus and other Greeks' ideas, probably as a result of extensive cultural interaction and trade between Greece and India prior to and during this time. For several thousand years, Leucippus' theories were forgotten – there would be those who would take up the concept of atoms and atomism and toy with it, but little came of it until about 1800 AD, when John Dalton, a British chemist, resurrected the ancient ideas and established the first modern atomic theory that was generally accepted. Any facets of his philosophy are still held in high regard today. Others, such as the idea that atoms cannot be created or destroyed, have been disproven. Our new atomic research derives from Dalton's resurrection and extension of ancient atomistic ideas.[1] 05

Democritus along with his mentor, leucippus. Lived on the basis of curiosity for atominism. However, Democritus, in terms of accomplishments, was more widely noticed than his mentor. And the lasting legacy of him is formulation of atomic theory, which later in more modern would inspire great physicists, like Newton to explore his curiosity and expand the boundary of human limited experience and knowledge. Though his work is highly praised by modern, at the time ancient Athens was largely neglected and disliked the personality of him. So much that Plato wanted to burn all Democritus’s books down. The idea that revolved around his writing was atomism, if compared to today's world. Is basically an observation to something move and unmoved, thus asking a question why it moves? And find out the reason behind, possibly, experimentation. In addition, his paper was trying to accent that the “final cause” or in more modern definition “purpose”. From this we can observe in physics from old to new time, always containing the text of science and human’s nature. In other translation would be for that the text of Physics and Psychics. Understand how one perceives and estimates the intention for those writings to obtain the full understanding, of all aspects that influenced the writer. Democritus was somewhat a subjective observer, and cultivated subjectivism. By that Democritus was a big picture who laid a fundamental for more objectivistic physics. 06

Dalton picked up the idea that has laid the foundation by Democritus, thus published his work for atomic theory, consisting of three prominent keys. First, all substances are made of atoms. Atoms are the smallest particles of matter. They cannot be divided into smaller particles. They also cannot be created or destroyed. Second, the atoms of the same element are alike and have the same mass. Atoms of different elements are different and have different masses. Lastly, Atoms join together to form compounds. A given compound always consists of the same kinds of atoms in the same ratio. However, 2 out of 3 conditions are pursued. But one is defied. It is that an atom is not the smallest particle, atoms consist of even smaller particles, we call it subatomic, like electrons, protons and neutrons. But these subatomic particles were not discovered until later decades by J.J Thompson. Then in very later decades, after the chemist Dalton, we have J.J. Thompson, who both discovered and experimented with cathode ray tubes. The experiment hypothesised that if an atom or atomic particles contain the charged ions, which are assumed that they have, it will create a magnetic field. This inference inspires Thompson to shine a direct ray of light through a tube that exterior is attached with a magnetic field conductor, like circuit for example. To see if the light would bend or not. When the light turns out bent, Thompson inference was sort of confirmed that these atomic particles contain subatomic particles that can be affected by magnetism. In accord to his inference, Thompson drew what we know as the “Plum pudding model of atom which inside contain “only electrons”. This was suggested for the time being. 07

Lastly, Rutherford, who picked up Thompson’s theory and proved that it is defiable. Rutherford and his gold foil experiment gave us further knowledge that an atom might not contain merely just electrons as for its subatomic particles. Rutherford, thus, conducted an experiment with inference that if Thompson plum pudding work, the Alpha ray that directed to the center of the gold, in his gold foil experiment, must not pass through or pass through as little as possible as most positive alpha rays might attach to “electrons”. But the result suggests otherwise, the ray slightly deflected on the side, few deflected back when hit the middle and some passed through the middle. Thus, Thompson recognised that atoms could not only consist of one subatomic particle. But contain two other more, the reciprocal to electrons, protons. This was because some of the protons travel to the middle deflect. And those that pass through, Thompson inference was that those protons might through neutrons, that does not possess and charge property, thus had no effect on those subatomic particles. For centuries, science has evolved into a form of complement to our intellect minds. Science such as physics gives us the explanation through the observation of scientists. With piles of documents, records, and knowledge, they thus synthesised to obtain the most simplified version possible to broaden and be accessible to all non-scientist audiences and readers. Each and every of the great scientists started off as a great observer, but they could never be great scientists at all if it was never for excellent articulation. 08

They spent much time for observation as for contemplation, to reduce their understanding into digestible size, and by that they write, they established reports, they announced data, and all for the eventual inheritage for future generations to discover and allow humans to explore for more understanding. Humans had always been knowledge-hungry creatures, desiring to understand the world around them, and the world beyond them. The universe, at large, is an area of study in which human beings are extremely interested in, as we humans, are just a tiny little part of this gigantic universe. It cannot be denied that all of us human beings are skeptical of how the universe works collaboratively to form things we see as normal in our daily lives, as we could not see them with our bare eyes. This is where the concept of Quantum comes in, to help us understand and conceptualize the little particles that exist within all beings, in space, to explain the unexplainable. 09

Classical Theories Versus Modern One's Uncertainty Principle, 1927 Werner Karl Heisenberg, theoretical physicist, awarded with a Nobel prize in Physics in 1932 [3]. He and his colleagues, Max Born[2] and Pascual Jordan[2], together, substantially elaborated the matrix formulation of quantum mechanics. And their first series of work together was in 1925,\"Quantum theoretical re-interpretation of kinematic and mechanical relations\" or in German, Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen.[4] Heisenberg’s paper laid the foundation of. A new theoretical “matrix mechanics,” new physics of the atom and its interactions that replaced the classical mechanics of Newton and Maxwell[4]. His paper of the uncertainty principle, is a non-technical summaries of nature for his non-physicist readers. However, Heisenberg admittedly was influenced by Newtonian and Maxwellian electrodynamics that had been seen as the foundations of all physics. Though his paper has brought new sensitivity to the field of knowledge. 10

Regarding, that the former theories comprised the parts of what later be defined by David Bohm[1], “Psychics,” and “Physics,”[1] these theories involved the concepts of force, mass, absolute space and time, continuous processes, causality, and an objective reality existing more or less independently of the observer[4]. During the early phase of his career as a potential physicist, Heisenberg met with Einstein and both became sort of close friends. They were even walking back together to Einstein's apartment. Heisenberg was fascinated by Einstein’s competence for literature and all sorts of popular paperwork at the time, such as Goethe, Schiller, and Humboldt. Their relationship would bring Heisenberg and Niels Bohr[5] to come and work together and produced several lasting paperwork until today. And as supposed to David Bohm, they create the terminology for “Copenhagen Perspective,” which is a certain set of attitude and logical analysis to view both the scientific observation and hypothesis. However, both parted away, since Bohr with allied nuclear project, and Heisenberg worked for Nazi Germany nuclear development. For those decisions made separately by two individuals shredded their relationship, and in good hope for physical development are less explored. In the later phase of Heisenberg’s life, his work is criticised and reviewed from time to time. One of prominent journalists, who elaborated Heisenberg’s conceptual principle of uncertainty and turned the principle into normal readable wording, David Bohm, played a large role in re-established and moderate Heisenberg’s political and philosophical views for life, thus his work would be appreciated with respect. 11

The uncertainties principle implied that ordinary objects are too small to be observed. As the principle became more definitive rule, thus, the complete rule suggested that the product of the uncertainties in position and velocity is equal to or greater than a tiny physical quantity, or constant (h/(4π), where h is Planck’s constant, or about 6.6 × 10−34 joule-second). For those who desire to measure the subatomic particles such as electrons, could not wish for more ambition. Because measuring each and every electron first is an equation, and as we thought we narrow the quantity to one, the notice would be that the electrons are unstable, never ever situated. Therefore, the principle by several observations concluded that simultaneous measurement for both position and velocity is quite doubtedly impossible. As position suggests where the subatomic particles might be, therefore the simultaneous attempt on velocity can be deviated. Why, satellite would be best analogy suit the explanation. The signal from satellite travel in wave form, and gives wavelength, same for these subatomic particles, once the signal is received the next signal is coming, so the current signal has gone, like movie, it keeps going unstop, so to pinpoint and measure how fast subatomic particles at the same time would only make us measure the past[6]. 12

Theory of Special Relativity, 1916 Albert Einstein was born at Ulm, in Württemberg, Germany, on March 14, 1879[6]. Six weeks later the family moved to Munich, where he later on began his schooling at the Luitpold Gymnasium. Later, they moved to Italy and Albert continued his education at Aarau, Switzerland and in 1896 he entered the Swiss Federal Polytechnic School in Zurich to be trained as a teacher in physics and mathematics. Why do we discuss Albert Einstein’s theory after Heisenberg, basically because the Heisenberg principle allows Einstein’s theory of relativity to enhance and be elaborated with some fundamental and not just some equation that comes out of nowhere[6]. Einstein was so pleased to have a debate and discussion with Heisenberg, because it helps him have a better understanding. So the same goes for other fields of science, the more you know the better. With several assists from Einstein, Heisenberg was able to become one of successful theoretical physicists. Einstein began thinking of light's behavior when he was just 16 years old, in 1895. He did a thought experiment, the encyclopedia said, where he rode on one light wave and looked at another light wave moving parallel to him. 13

Classical physics should say that the light wave Einstein was looking at would have a relative speed of zero, but this contradicted Maxwell's equations that showed light always has the same speed: 186,000 miles a second. Another problem with relative speeds is they would show that the laws of electromagnetism change depending on your vantage point, which contradicted classical physics. Therefore, Einstein’s ambition was to be able to defy Maxwell’s equation[7]. At the start of his scientific work, Einstein realized the inadequacies of Newtonian mechanics and his special theory of relativity stemmed from an attempt to reconcile the laws of mechanics with the laws of the electromagnetic field. He dealt with classical problems of statistical mechanics and problems in which they were merged with quantum theory: this led to an explanation of the Brownian movement of molecules. He investigated the thermal properties of light with a low radiation density and his observations laid the foundation of the photon theory of light[7]. Bit of rewind, with a brief description of his work above, connect this to Heisenberg’s principle, and it would be strangely but accurate elaboration to Einstein’s research and observation. Thus, later in life of Einstein, he made sense out of his curiosity, and today the world pursues complete understanding of theory of special relativity, physicists would remind themselves of Heisenberg’s principle while applying new approaches and factors to the equation. And say who helped Einstein perfect his equation, it would not be if it was not for Erwin Schrödinger’s cat[8] thought experiment. In 1927 Schrödinger accepted an invitation to succeed Max Planck, the inventor of the quantum hypothesis, at the University of Berlin, and he joined an extremely distinguished faculty that included Albert Einstein.However, Schrödinger, we’ll be talking about him later. 14

What Einstein introduced to the world of Physics was a true excitement, because the equation proved to be definable to Maxwell’s equation, however it did not eradicate the fundamental Maxwell gave. But, Einstein, with his own sets of data and knowledge. It was possible for him to form an equation. However, if this is not clear enough these two pictures might help elaborate the equation. Supposed you watch on space, the cat gains energy and loses energy by the conservation of energy law. So the velocity of the cat would not change. The theory suggests that when we measure energy of the light, time for us and the cat is different because of the frequency. And that we call the Doppler effect. The idea here can be elaborate into an equation. Which m = mass, c2 = the speed of light squared and E = kinetic energy.[7] 15

Einstein responsible for Hiroshima and Nagasaki? What you’re looking at right now, is just a few seconds after the A-Bomb landed on the japanese soil, Hiroshiman, on August 6, 1945. It was the first remark of the outcome from both metaphysics and quantum physics that contributed. But one would wonder how. When it comes to the question, again and again, people pinpoint the man who formulated the equation, Einstein. But was Einstein responsible for, debatable, but apparently, in the modern world, one might give analogy to drug dealing. Selling drugs is as illegal as consuming it. The same with E=mc2. The man who gives the equation is no different from the murderer with indirect acts. That’s the actuality the oppositions address in a debate. However, what can normal people like non-scientist think of this, immoral, brutal, or solution? So what the other side thinks, the other side definitely has a strong stance on the debate that Einstein was a pioneer and never to become the murderer. There are several other Nazi German Physicists, like Heisenberg, Schroedinger, and other more. Meanwhile, a guy across the continent in America, like Oppenheimer who advanced the formula, and exploited the great knowledge in the future for development of Hydrogen-Bomb, though his stance was opposing the project for offensive related purposes. What do you think, are these guys equally responsible?[9] 16

Schrödinger Cat, 1935 What Schröedinger threw into the conversation was his philosophy of what we call today Schröedinger’s cat thought experiment. Basically, it suggests that when we think of quantum physics, it is fundamental to keep in mind that the perspective of your observations is different from the subject observation. His point of view is a basis of objectivism. Objectivism, which defines the specific way to approach physics behind curiosity. The experiment states you place a cat in a box with a tiny bit of radioactive substance. When the radioactive substance decays, it triggers a Geiger counter which causes a poison or explosion to be released that kills the cat. The cat ends up both dead and alive at the same time. What does it mean simultaneously, the possibility can be elaborated two ways, cat’s perspective and you and the cat. You can only accept that the cat survived or died. However, the cat can observe the internal system, it can either survive and see the explosion or no explosion at all, if the atoms decoy first. Or else it dies and sees the explosion. So it suggests that physicists must try to understand not only what they come across with but also what the subject could possibly encounter and react with[8]. 17

Erwin Schrödinger was born on August 12, 1887, a Nobel Prize-winning Austrian-Irish physicist who developed a way to calculate the wave function of a system. In early time, they did not possess an oscillator machine, which would produce a consistent graph without a distraction of slight small earthquakes that happen constantly, but purely the electromagnetic field.[10] The machine they used at the time, was a machine that relies on the vibration of the needle to draw up the frequency of certain subject of measurement which often proved today to be inaccurate since there are uncountable possible factors affecting the eventual product of wavelength and imprecise frequency. Regarding that the machine for lie detector and wave machine can measure impulse since impulse is also one form of expression that can be displayed in wave form. 18

Waves are characterized by their repetitive motion. Imagine a toy boat riding the waves in a wave pool. As the water wave passes under the boat, it moves up and down in a regular and repeated fashion. While the wave travels horizontally, the boat only travels vertically up and down. A wave cycle consists of one complete wave— starting at the zero point, going up to a wave crest, going back down to a wave trough, and back to the zero point again. The wavelength of a wave is the distance between any two corresponding points on adjacent waves. It is easiest to visualize the wavelength of a wave as the distance from one wave crest to the next. In an equation, wavelength is represented by the Greek letter lambda (λ).Typically, frequency is measured in units of cycles per second or waves per second. One wave per second is also called a Hertz (Hz) and in SI units is a reciprocal second (s−1)[11]. 19

Bohr developed the Bohr model of the atom, in which he proposed that energy levels of electrons are discrete and that the electrons revolve in stable orbits around the atomic nucleus but can jump from one energy level (or orbit) to another[12]. Niels Henrik David Bohr, 7 October 1885 – 18 November 1962) was a Danish physicist who made foundational contributions to understanding atomic structure and quantum theory, for which he received the Nobel Prize in Physics in 1922[13]. The Bohr Model is a modification of an earlier atomic model, the Rutherford Model. The Bohr Model has an atom with a positively-charged nucleus surrounded by negatively-charged electrons that have circular, planetary-like orbits. Today, we know that the Bohr’s Model has some inaccuracies, but it’s still used because of its simple approach to atomic theory. The Bohr model was also the first atomic model to incorporate quantum theory, meaning that it’s the predecessor of today’s more accurate quantum-mechanical models. In the Bohr model, the electrons travel in defined circular orbits around the small positively-charged nucleus.with a positively-charged nucleus surrounded by negatively-charged electrons that have circular, planetary-like orbits. Today, we know that the Bohr’s Model has some inaccuracies, but it’s still used because of its simple approach to atomic theory[14]. 20

The Bohr model was also the first atomic model to incorporate quantum theory, meaning that it’s the predecessor of today’s more accurate quantum-mechanical models. In the Bohr model, the electrons travel in defined circular orbits around the small positively-charged nucleus. 21

MODERN irst of all, the concept of physics and chemistry currently is to justify and to discover the underlying applications in reality and incidents that happen around us. New theories, laws, and rules in physics and chemistry are established to interpret many aspects of the world in a fundamental and accurate way by using technologies and machines. Subsequently, the inquiry of theory motivates thinkers to discuss and debate, resulting in an agreeable understanding and theory or merging one hypothesis to another for connection of the better. Some covers in a large scale, but some covers in a smaller scale that is complex to observe. Various attempts were employed for experiments and researches to prove the truth of what was behind those theories. Hence, the theory of quantum mechanics is the aspect that is emphasized on its smallest scale. Stephen Wolfram, a British-American physicist, computer scientist, businessman. , is known for his achievement in simple algorithms. He is known as an inaugural fellow of the American Mathematical Society, and is known for his knowledge and project on mathematics, computer science, and theoretical physics. Working with other collaborators in emphasizing space-time curvature and relativity, he concluded quantum mechanics as an emergent characteristic of identical universes. 22

He, then, indicated the connection of relativity and quantum mechanics, which raised an prominent and critical idea in recent physics called computational complexity. The new theory that he came up with is the three pillars of modern physics, consisting of computational complexity, relativity, and quantum mechanics. To justify, his any new theory is testable predicted measurement. Thus, a path to the fundamental theory of physics.So what does today modern physics is working on, they’re basically developing the mechanics and providing more understanding to those theories pioneered by so called classical theorists. To explain in details would require so many pages, but to sum up the progress related to each topic mentioned. 23

ELECTRIC POWER PLANTS Electric Power Plants[17] have a number of components in common and are an interesting study in the various forms and changes of energy necessary to produce electricity. 24

Boiler Unit: Almost all of power plants operate by heating water in a boiler unit into superheated steam at very high pressures. The source of heat from combustion reactions may vary in fossil fuel plants from the source of fuels such as coal, oil, or natural gas. Biomass or waste plant parts may also be used as a source of fuel. In some areas solid waste incinerators are also used as a source of heat. All of these sources of fuels result in varying amounts of air pollution, as well as, the carbon dioxide. In a nuclear power plant, the fission chain reaction of splitting nuclei provides the source of heat. Turbine-Generator: The super heated steam is used to spin the blades of a turbine, which in turn is used in the generator to turn a coil of wires within a circular arrangement of magnets. The rotating coil of wire in the magnets results in the generation of electricity. Cooling Water: After the steam travels through the turbine, it must be cooled and condensed back into liquid water to start the cycle over again. Cooling water can be obtained from a nearby river or lake. The water is returned to the body of water 10 -20 degrees higher in temperature than the intake water. Alternate method is to use a very tall cooling tower, where the evaporation of water falling through the tower provides the cooling effect. 25

Or to put modern physics into simple words, is like comparing Black-White sepia photo to brightful color pigmented picture. In modern physics, as mentioned, refined and redefined the former laws and theories to make it applicable as correlation to today's world technological advances. During those twentieth century, physicists and chemists were not having these technologies, which would essentially help them explore the atomic world or as a more complicated term, the Quantum realm. So what’s the desire of the modern world, unlike before, it was a discovering period, scientists were so perpetually proposed and introduced their laws and principles, as explanation to their observations. But now with machines and technology which some might say allow a walking creature to observe these minor details of our world, in order to produce a sustainable way for beings to live in a world that hopefully has less pollution, more understanding and large aspects of life. Like Wolfram, his initiative is to create the testable measurement, which fundamentally and mechanically provides us the correction to the system that will be applied to certain daily activity. Also mentioned already, creating free and unlimited electricity by nuclear power plant, for example, during USSR time, the power plants were introduced quite nationwide, and the tragedy dummy test with the neighborhood of Chernobyl, the explosion of being long eradicating remained radioactive nuclear. Or like in the movie Angels Demons, the interaction of quantum energy, the slightest and smallest particles but can produce high and long lasting energy. And with the great possible threat of explosion. So they’re testing to stabilise and keep the energy contained with the safest measure. 26

What is Quantum Theory? The story of the birth of the universe has many interpretations, whether from the viewpoints of religion, science, or spirituality. How did this elusive world come to be? Even after several thousand years of recorded history, human beings’ mulling over the reason for our existence, the origin of our existence had never really bore fruit. While we understood more and more of the world around us, there was naturally a limit of which we would reach without exhausting our resources on a branch of science. This was what happened during the 19th century when all questions that were answerable by classical physics and chemistry were answered, and the questions unanswerable remained unanswered, hence the need to birth a new branch of science completely. This is how Quantum came to be. Quantum Theory is the theory that deals with the behavior of matter and light on the atomic and subatomic scale, or basically on the smallest scale. In all actuality, Quantum Theory is the combination of various theories that are applied to different types of phenomena that humans cannot see, through the usage of physics and quantum hypotheses. Of course, the definition of Quantum Theory is still highly debatable to this day, being a topic that is both elusive and extremely vague as it covers a scope that is large in quantity, but small in terms of individual size, making it hard to believe and understand. It does not help that more often than not, the concepts behind the theory often clash with what we consider the norm, the common sense of the things we see by eye. 27

History of Quantum Theory Quantum theory was born out of necessity, as by the time of its conception, classical physics had practically solved most of the problems solvable by classical physics already, and the other unanswerable questions just stubbornly refused to be answered by normal means. This made the physicist during the time confused, unaware that the answer to the questions was something that would revolutionize the way we understand the world. But in order to look forward, we should look backward first, to what had marked the beginning of the new field of physics called Quantum Theory. Initially, scientists in the 18th century believed that light consisted of particles, or corpuscles, as predominantly influenced by sir Isaac Newton himself though many had come before him to discuss the properties of light. Newton’s predecessors, the philosophers of ancient Greece, laid much of the foundation that led to Newton’s theory about light, and though his views were of the mainstream during his time, his views were opposed and contested by a physicist from dutch named Christiaan Huygens. Huygens believed that light was, in fact, waves, rather than the particles that Newton had claimed. Eventually, his views became the mainstream, but it wasn’t until doctor and physicist, Thomas Young, who claimed that his experiment was something that ‘may be repeated with great ease, wherever the sun shines,’ came and proved the theory true. 28

The experiment that debunked Newton’s claim was now called the double-slit experiment, where if light passes through a pair of slits, the light will interfere with each other and cause a fringe-like pattern with alternating bright and dark bands to appear on a screen. This is explained by the wave theory of light, where if the waves arrive together in the screen then a bright band would appear, while if the light arrives at the trough of the other beam then it would cancel each other out and become a dark band. After Thomas Young, there were many people who continued proving the wave theory of light, starting from Francesco Grimaldi’s first observation of what would become what Augustin-Jean Fresnel proved as diffraction, which is when a parallel beam of light passes through a slit, the rays that emerge will start to diverge, to other people who help contribute to the making of the wave theory of light. This also extends to James Clerk Maxwell, a theoretical physicist who predicted the existence of electromagnetic waves, and the famous Albert Einstein who discovered the photoelectric effect theory (image on the next page), which predicted that light is made up of particles called photons, of which had the properties of a wave. Einstein also discovered the theory of Brownian motion, which said that molecules move randomly which provided evidence for the particle theory, and the theory of special relativity, which talked about electromagnetism and solved the problem in 19th-century physics. 29

The question is, how did Quantum theory develop from the wave theory of light? The wave theory of light, despite covering many grounds that explain the interference (effect of combining two or more waves moving on paths that intersect or coincide with each other which causes the amplitudes to react at each point depending on the frequencies of the wave involved), and diffraction, they don’t actually cover the aspect of which was the absorption and emission of light. During the 19th century, there had been many attempts to try to calculate the energy distribution within a blackbody (a hypothetical ideal body that can absorb and emit all the light energy that falls on it) through using classical physics, though all of them had failed miserably. This failure was because all of the physicists who attempted to solve the problem had assumed that the atomic vibrations were continuous, which meant that they could vibrate at any frequency. 30

This assumption was made with the limited knowledge of physics in that time period, and the person who ultimately solved the problem, Max Planck, solved it by taking a standpoint that was seen as risky at that time. He, using the idea that the atomic vibrations were emitted at a certain frequency, in packets called quanta, discovered what would become an integral part of Quantum, Planck’s constant. It was first used in Planck’s law, of which the equation of the Planck’s law is E=hv, with h being Planck’s constant with the value of roughly 6.626 x 10⁻³⁴ m² kg / s. This assumption bore fruit, and Planck was able to conclude that atoms can only take on certain values, and that atomic vibrations are quantized. Planck’s discovery would lay the foundation for the topic of this paper, Quantum. 31

Quantum Theory to Quantum Mechanics In Quantum theory, there are 3 themes: the quantization of energy, the particle nature of a matter, and Planck’s constant. These 3 themes, when used together, create a web of related theories that lack the clarity, coherence, and system of mathematical equations that is required to form a theory. This is where the idea of Quantum Mechanics comes in. Quantum mechanics is something that was developed as a necessity in order to prove Quantum Theory, and it is defined as something that can successfully prove a concept that is largely hard to understand mathematically and make sense of the observations that was given by its predecessor, Quantum Theory. Shortly after the development of the Quantum theory by the combined efforts of over 30 years by scientists, following Albert Einstein’s theory about the Photoelectric effect, Ernest Rutherford’s discovery of the nuclear atom, and Niel Bohr’s Model, Quantum Mechanics was first used when it was theorized that sometimes, light waves exhibit particle-like activities, and on some occasion, particles can exhibit wave-like behavior. This theory was confirmed and proven by formulations that would help define Quantum Mechanics, and following this was Schrodinger’s wave mechanics, which used the wave function to define the probability of finding a particle in a point in space. 32

Another similar theory was developed around the same time by Heisenberg, the matrix theory, and though there was no mention of wave mechanics, it was shown to be mathematically equivalent to its Schrodinger's own. He, using the philosophical notion that in order to explain unobserved events, he had to first have a clear and precise understanding of an observable event, he discovered the uncertainty principle. Uncertainty principle was a principle which stated where for certain pairs of observable factors, their product of uncertainties is, at the very least, as large as Planck’s constant. The pair of observables that exhibit this trait are called incompatible observables, and as a direct consequence of this principle, it meant that the reduction of uncertainty in one observable factor meant the increase in another. This thought was an important idea in the field of quantum mechanics, because this led to the acceptance of the modern description of atoms. Albert Einstein’s successful proving of the photoelectric effect theory was something seen as revolutionary, something that had helped set the scene for Quantum Mechanics and still remains a central concept of Quantum Mechanics. Despite not being the person who outright discovered the photoelectric effect, he had been the person who solved the paradox that was the effect. This discovery of his, uncovered the nature of light by describing them to be composed of quanta, or now known as photons, which rectified the view that light was a continuous stream of waves. This discovery led to the betterment of the understanding of the dual nature of light, and it is also used to investigate energy levels in matter. 33

If there was another pair who could be considered the pioneers of Quantum Mechanics, it would be Ernest Rutherford and Niel Bohr. As mentioned earlier, Rutherford was credited with the discovery of the nuclear atom, and as a branch of physics that is built upon the study of molecules and the unseeable, this discovery was a significant find. He had proven that the plum pudding model that came before him wasn’t quite right, and that the atom must have a central nucleus, and that all the electrons orbit around the nucleus like our solar system. This was almost right, and Bohr came along to fix the assumption ever so slightly by applying Planck’s theory to the atoms, and concluding that the electrons ‘jump’ between orbits. While this thought wasn’t widely accepted in his time, it eventually paved the way for Quantum Mechanics to develop into many other branches that can be applied to a variety of subjects. 34

Quantum Chemistry There are many branches of Quantum Mechanics, and it can be used in various fields, not limited to physics alone. A branch of this which eventually developed to be more centralized around the study of molecules and how they interact with each other is called Quantum Chemistry, or also known as Molecular Mechanics. Quantum Chemistry is basically the application of quantum mechanics to the study of molecules, which is mainly used in the field of, well, chemistry, to predict the chemical and physical properties of molecules and materials. This branch was a theoretical and computational challenge to the chemists who tried to tackle it, but the impact that it had was very well worth it. Before we could talk about the impact it has on the world, we have to understand the bare basics of chemistry by defining what exactly molecules are. Molecules are particles made of 2 or more atoms, held together by a chemical bond. It does not matter what elements they are made of, the same or different, they are still considered a molecule. They are held together by 2 types of bonds, covalent and ionic. Historically, molecular theory and atomic theory always came hand in hand, as matter has been theorised to be made up of ‘discrete’ units during Ancient India, and then in Ancient Greece, Leucippus and Democritus coined the term ‘atomos’, which referred to the smallest indivisible parts of matter, though these concepts never really entered the field of science until the late 18th centuries when the Law of Conservation of Mass and Laws of Multiple Proportions eased them in. 35

Application for Quantum Mechanics The invention of the Scanning Tunneling Microscope (STM) allowed atoms and molecules to be observed directly, which only helps our understanding of the molecule. But it is definitely the conception of quantum mechanics that really helps us understand the concept of molecules. Much of the information about the atomic structure has been discovered through the help of quantum mechanics, as quantum models have made predictions about the pericyclic reaction among others, which helped enrich the knowledge of chemistry, and sometimes, even revision of the understanding. Of course, some may argue that the understanding of chemistry itself was what lent to the development of the quantum models in the first place, but the study of quantum and chemistry had been interlocked ever since its conception. The usage of quantum mechanics on the periodic table provides the ability to specify and explain the atomic structure of an element, and provide a reason why each element is in its respective vertical and horizontal columns. Though the periodic table had existed for longer than quantum mechanics had, it is undeniable that quantum mechanics are extremely helpful in classifying elements according to their chemical and physical properties. 36

Not only that, quantum mechanics had enriched the understanding of molecular structure through the conclusions drawn from different quantum models. Inventions like the molecular orbit (MO) had revealed effects previously unseen by the electron delocalisation on the stability of a molecule. In a sense, Quantum mechanical models had been developed through the help of classical theoretical chemistry, in the way that the models are created, corrected, and calibrated through the existing knowledge of chemical postulations or the knowledge from chemistry. In Quantum Chemistry, the one thing that serves to be the most important part of it is definitely Bohr’s model, or his theory of the hydrogen atom. His model only required 1 assumption, which was that the electron moves around the nucleus in circular orbits that can have only certain allowed radii. Although his assumption of the circular orbit was proven false, he managed to propose a thought that electrons could only occupy certain regions of space. His theory explains the emission spectrum of the hydrogen atom, and this would be used in electron transitions, giving birth to contemporary applications like telecommunication systems like cell phones, or Global Positioning Systems like GPS. 37

Problem about Quantum Quantum Theory, while widely accepted and used by physicists and chemists all around the world for various applications, had many problems attached to its coattails. The theory itself covers extremely wide fields of applications and usages, almost too wide in fact, that it is considered an indeterministic theory. This means that while we know of the current state of some atomic system, this does not mean that we know its future as it is not fixed in stone. A particle may be somewhere without being at any particular place, and may have energy and momentum without having a specific value for them. Another problem that seems to exist in this is the amount of possible interpretations which could describe the theory. The interpretation in which we use to describe the mathematical equations we receive from the usage of Quantum Mechanics varies from situations to situations, though it is not to be misunderstood that the problem lies in the equations. The variable that differentiates the interpretation involves what is added to the ‘common core’ of the experiment, or basically the recipes for calculating probabilities of the outcome of the experiment performed on systems. Not only that, Quantum Mechanics had enriched the understanding of molecular structure through the conclusions drawn from different quantum models. Inventions like the molecular orbit (MO) had revealed effects previously unseen by the electron delocalisation on the stability of a molecule. 38

Problem about Quantum The problem that Quantum theory faces is called the ‘measurement problem’. The measurement problem is described as a logical contradiction between the laws that describe the motion in quantum systems. Even as we use quantum mechanics to prove the theory, no matter how successful it may have been in doing so, there is still no discoverable way to predict when the functions stop evolving in a united function and collapse. In terms of interpreting the state, if we were to take the quantum state to be a complete description of the system, then the state is not corresponding to a definite outcome. This led J.S Bell to remark that, ‘Either the wavefunction, as given by the Schrodinger equation, is not everything, or it is not right”, in which he remarks that the wave function did not cover all the circumstances that revolve around quantum theory. This would branch on to 3 ways to approach the measurement problem. The first would be to deny that the wave function yields a complete description of a system. In this category of approach would deny that a quantum state should be thought of representing anything in reality at all, and would include variants of the other types of anti-realist approaches, like the Copenhagen Interpretation. The second is to say that the modification of the dynamics, in appropriate times, to produce a collapse of the wave function, is required. This would motivate research to find the suitable method of modification to the dynamic, of which would often be referred to as the ‘hidden variables’. 39

Problem about Quantum In this, many theorems attempt to pinpoint and quantify the possible hidden- variables, attempting to create a theorem that would assign the quantum observable variables with definite values that would be revealed upon measurement. This would make the measurement of the observable part yield the definite value assigned to it. These theories are called the non-contextual hidden variables theory. Other theories to supplement the quantum state with additional structure would be called the modal interpretations. Then,the last way to approach the measurement problem would be to reject both views completely, with the belief that the quantum state is complete hence ignoring the problem completely. 40

PLANCK’S CONSTANT Quantum Theory, and then later Quantum Mechanics, was developed through the help of countless physicists over the span of centuries and centuries of trial and error, but if we were to speak of someone who truly helped ease the transition completely, whos discovery is a large part of the theory itself, it would be Max Planck, a German theoretical physicist. Full name Max Karl Ernst Ludwig Planck, or better known as Max Planck, holds a Nobel Prize in Physics 1918 for his discovery of the energy quanta that helped advance physics to a higher level. He started out on the path of research on the subject of thermodynamics, which was something he held much interest for under the tutelage of Kirchhoff and Helmholtz. He published various papers under the topic of entropy, thermo electricity, and others, and while his work was well received, he didn’t really achieve any breakthrough from his results that was worth noting down. 41 QUANTUM 2021

This was when the problems related to the radiation processes caught his attention. Later dubbed the Ultraviolet Catastrophe, the physicists during that time were having a discussion regarding the distribution of energy in the spectrum, as the explanation provided by classical physics had not measured up to the trials of experimentation. The Rayleigh-Jeans law, the explanation provided by classical physics of the time, only worked when the frequency of the light emitted from the blackbody is low, and not high. High frequency of light waves is defined as Ultra Violet, hence the name, ‘Ultraviolet Catastrophe’. Planck, using a last ditch method by assigning an energy unit to a given frequency and using multiples (a quantum, as he would call it, a whole number, not one and a half or pi) , was able to solve the underlying problem of the Rayleigh-Jean Argument. By creating a constant, he was able to convert the frequency to energy, hence being able to have a small but finite value to get the right formula to solve the problem. The formula that Planck had created is called Planck’s Equation, being E=hv, where E is the energy of the photon, v being the frequency of the photon in Hertz (Hz), and h which was Planck’s constant. 42

His discovery would mark the turning point of classical physics, giving birth to a new and more elusive branch of physics itself, Quantum. The discovery would give way to Einstein to detect the nature of the photon, defining it as the fundamental particle of light or quantum. The photon itself can be absorbed or released by molecules and atoms by passing the energy of a photon to either one as it is absorbed, making the formula capable of being used in reverse as well, such as when the molecule or atom loses its energy to release the energy. While Max Planck’s scientific career was marked with incredible success, his personal life had been something like a tragedy. He married twice, first with his childhood friend from his hometown, Marie Merck, who eventually died 24 years into their marriage, then he remarried her cousin Marga von Hosslin. He had 5 children, 3 of which died young and another died when 1 of the 2 of his surviving children was executed for his part in the attempt to assassinate Hitler. During the time of World War II, he had been an outspoken opposer to the treatment of Jews by the Nazi government, yet remained in the country due to his feeling of duty. His house was bombed during the last weeks of the war, making life hard for him. To the people who knew him, they remembered him as a man worth remembering, not only because of the importance of discoveries to the scientific community, but also for his great personal qualities and morals. He was known to be a gifted pianist, who would’ve become a musician had he not had his passion in the sciences. 43

What is it? Planck’s constant, or the symbol h, is an integral part of Quantum Mechanics, and arguably the most important one. It is a physical constant, used to describe the behavior of particles and waves on the atomic scale, including but not limited to the dual nature of light. The constant quantifies to roughly 6.626 x 10-34 m2 kg / s. In other words, the product of energy compounded by time is known as action quantity, thus, Planck’s constant. Planck’s Constant Equation As mentioned before, Max planck experimented on the hypothesis of absorbing and emitting light energy, also, known as black-body radiation principle. To emphasize, black-body radiation is defined as a system that absorbs all radiation or spectrum of light reflecting on it in the same manner as they re-emit the radiation, resulting in an absolute emitter and absorber. Planck then justified his math principle by saying that light energy existed in discrete numbers, or quanta, instead of in continuum. Winning a Nobel Prize in Physics, Planck invented an equation connecting the following principle of energy quantum to the Rayleigh-James law, the Stephen- Boltzmann law, and the Wein’s displacement law, thus, creating E = hv pr the Planck- Einstein equation. E is the energy changes, v is the oscillation frequency of the particle, and h is the Planck’s constant as mentioned earlier (which has a value of 6.626 x 10-34 J s or m2 kg / s) 44

For instance, to find the changes of photon energy from a light’s wavelength of 682 nm, basically, we need to find the frequency of light particles using wavelength and frequency equation, which is c = λ������. Firstly, we isolate by rearranging the standard equation then convert nanometer to meter by dividing 109 to 682 nanometer. 45

Uncertainty Principle In Planck's Constant 46

Introduction To Waves A repeat, high or low, disturbance that moves through space or a physical medium is a wave, such as a light wave, sound wave, and ocean water. To demonstrate, a graph of sine can emphasize the image of the wave better as shown below. The image shows how waves work regularly. The wavelength (λ) indicates one cycle of the wave before a new identical cycle starts and ends next constantly, regardless of any other disturbance. Its SI unit is meters (m). Hence, the time drawn from the start to the end of the cycle or in one cycle is called a period (T). Moreover, an amplitude indicates the distance between a crest or the trough of the wave to the average value of y as shown in the graph, so, basically, it determines the vertical length of a vertically half of the wave. For a matter of fact, since the wave fluctuate at a given position at a certain time and space, it is known as the quantity called frequency (������ or ������). Frequency is defined as the number of entire wavelength that identically repeat at the same point every second; with a SI unit of Hertz (Hz) or per second (s-1). Thus, it can be concluded that the bigger the wavelength, the smaller the frequency as demonstrated in the picture below; meaning that frequency and wavelength are inversely proportional. 47

c = λv The following equation represents the relationship between wavelength, frequency, and c, which is the constant of the speed of light of 3108 m/s. Additionally, it demonstrates how the speed of light refers to all electromagnetic radiation, regardless of frequency or wavelength. For instance, to find the frequency of a electromagnetic radiation wave with a wavelength of 4109 m, we begin with arranging the equation in an appropriate form to find the frequency. Step 1 Rearrange the equation Step 2 Substitute the quantity of a given wavelength and the light's speed constant to the equation, and solve for the answer Thus, the frequency of the given electromagnetic wave is 7.5 10⁻² s⁻¹. 48

As shown in the above figure, wavelength and period are slightly different if you look closely. Wavelength considers the distance between identical points of the wave, while period considers the time between them. The following equation indicates the relationship of the period and frequency, which is inversely proportional. The period is the reciprocal of the frequency of the particular wave at the given time. 49