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Photoelectric Effect

By Piyush Daigavhane

In 450 BC, the great Greek philosopher Zeno was puzzled by a thought experiment in which he assumed himself to go to the garden. He divided his path into infinitely small distances;to cover those infinite parts he would have required infinite time, but that was not the case. This is often called the Dichotomy Paradox. There surely is a problem with this paradox and one of them is that Zeno assumed space to be infinitely divisible. In this way, Zeno questioned a very rudimentary idea of the scale of the quantum world that we know today.

Max Plank and for that matter the entire scientific community was puzzled by the black body radiation’s graph that was based on experimental analysis, because none of the scientists were able to explain the hill shaped graph mathematically. Two English scientists Sir James Jeans and Lord Rayleigh, in order to explain the phenomena, introduced the law of equipartition. They were able to explain the graph for small frequencies, but their predictions for high frequencies, like the visible and ultraviolet spectrum, were very absurd.

According to them, the intensities should eventually approach infinity as the frequencies increase. Rayleigh-Jeans calculation allows particles to vibrate with any amount of energy all the way to distribute to infinitely tiny wiggles. When they try to distribute energy to equipartionates across the possible energy states, way too much energy gets packed into countless very tiny energy states at high frequencies. Mathematically, they were trying to find time required for Zeno to cross those infinite parts of path to reach the Garden, eventually never reaching the garden.

To counter this, Plank found a way to calculate the total energy of molecules, which according to him, was very silly. He assumed those particles to vibrate with energies that were multiple of some minimum energy states(which later become Plank’s Constant). In simple words he quantised the energy states and with this assumption was able to explain the experimental graph very accurately. He was very reluctant with the idea of quantizing the energy states, but it somehow explained Black Body Radiation.

In 1902, Lenard published his observation on the photoelectric effect. His results were unexpected, when he increased the frequency of light moving from infrared heat and red light, up in frequency to violet and ultraviolet, the Electrons sped out with much more energy, ultimately increasing the intensity of light by using a carbon light arc that could be made brighter by a factor of 1000. The brighter, more intense light had a lot more energy, so it seemed logical that electrons emitted would have more energy and speed away faster, but that did not occur. More intense light produced more electrons but the energy of each remained the same. This was something that the wave theory of light did not explain.

The observations made by Lenard became very famous and now it has become a race in the scientific community for who can explain the effect.

Einstein had completed his undergraduate in 1900, and now was looking ahead for a Doctorate, he had been keeping a keen eye on current advancements in physics. 1905 was going to be a miracle year for him. His first paper described his particle theory of light, which also explained the photoelectric effect. This paper later became one of the most fundamental pieces of writing for modern physics.

He proposed that light is made up of discrete particles or packets of energy , which is a multiple of Planck's constant. He used this idea to explain the phenomenon of photoelectric effect. According to him, if light came in discrete quanta then the energy of each one was determined simply by the frequency of the light times Planck's Constant. Assume that light transfers its entire energy to a single electron, then it follows that light of a higher frequency to cause the electrons to emit with more energy. On the other hand, increasing the intensity of light (keeping frequency constant) would simply mean that more electrons would be emitted, but the energy of each would be the same. This was precisely what Leonard had found .

This paper made Plank furious. According to him, Plank’s constant was a constant energy released or absorbed by vibration of molecules. The quantum was a mathematical contrivance that explained how energy was emitted and absorbed when it interacted with matter. but he did not see that it is related to a physical reality that was inherent in the nature of light and electromagnetic field itself. But Einstein's statement clearly mentioned that energy carried by any radiation was multiple of this constant.

The Plank’s constant became very common in essentially all equations that described Quantum phenomena. For example, the Heisenberg Uncertainty Principle, de Broglie wavelength, Schrodinger's equation, energy level of electron Orbit and the relation between energy and the wavelength of light.

Einstein's theory and formulas of photoelectric effect was later proved by Robert Millikan and yet he still rejected the theory. After 1920 and the coming subsequent years, Quantum theory was being accepted by most of the scientific community. Even if Einstein founded an important part of Quantum theory, he still had this fundamental question: “what exactly are light quanta”.

Photoelectric effect was explained assuming that light is a particle which in itself was a very revolutionary idea. For the explanation of this phenomena, Einstein was awarded the Nobel Prize in 1921. The idea that light can also be a particle was hard to digest because it violated the laws of classical physics, in which everything can be divided infinitely and there is no smallest quantity. In the following years, more experiments were carried out to verify the particle nature of light, one of those experiments is Compton scattering experiment which was performed by Arthur Compton and De Broglie also proposed an equation stating the dual nature of light in 1923, which further made the case evident.

Einstein had a very curious mind, and he believed that curiosity is must for any endeavors and with this thirst for knowledge anyone could become a genius.

Observing nature and trying to replicate it is really amazing and sometimes utterly complicated. There's some pattern in everything we watch, governing the evolutionary history and survival of every biotic and abiotic thing in this universe. Some have a similar pattern and some don't, but still many times a narrow bridge can be constructed to relate them and that is the essence of the nature of the universe. "Look deep, deep into nature, and then you will understand everything better" were his words to his son Hans. These words really have great implications in the modern world, where our mind is occupied with endless thoughts and we barely are able to appreciate the offerings of nature. I hope that the present and the coming youth develop these very basic but powerful skills to observe their surroundings and nature, and this would surely bring new breakthroughs at an exponential rate and benefit humanity.


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