The Quantum Theory of light

 

Introduction

This time in the form of light quanta and learn how it provides an elegant interpretation of max Plank's blackbody radiation solution. We'll also learn how the discovery of light's particle nature can be tracked back to the very experiment that proved it was a wave.

We'll be formally introduced to Albert Einstein and see how he revived a concept promoted fruitlessly by his esteemed predecessor, Isaac Newton. You will learn about the photon and its important physical properties and discover why it evaded detection for so long despite its ubiquity.

Finally, We'll begin to explore the first of the great logical inconsistencies of quantum physics, wave particles duality and see the extent to which physicists have come to grips with it more than a century after its discovery.

Fig: Photoelectric Effect 

 Maxwell Stumbles Again

We know that Planck's constant is named after him. Likewise, the strength of forces is measured in units named after Newton. So you shouldn't be surprised  to learn that the physicists unit for the frequency of light waves is named after the man who first demonstrated that light really is a wave - Heinrich Hertz.

Through a series of exceptionally challenging experiments, Hertz demonstrated in the laboratory that oscillating charges emit waves that moves exactly the way Maxwell predicted about 15 years before. How ironic, then that Hertz stumbled upon and then brushed aside, a side effect that would eventually demonstrate that light is not q wave after all or at least not all of the time.

Hertz created radio waves  in his lab by charging a pair of metallic spheres so much that s huge electric spark would jump from one sphere to the next, He found that he got the juiciest sparks when he kept the spheres nicely polished. He also found that ultraviolet light shone on the negatively charged sphere, the sparks, the sparks flew all the easier.

Since this effect linked both light and electricity, it was christened the photoelectric effect. About 10 years later, after J.J Thomson had discovered the electron, it was recognized that the spark between the spheres was basically a stream of electrons. This led to a physical interpretation for the effect of ultraviolet light on the sparks. If the light delivered enough energy to electrons residing within the metal, the electrons residing within the metal, the electron could escape the atoms to which they were bound. A fixed amount of energy was required to liberate the electron in the first place, and any extra energy would be carried away by the liberated electron in the form of kinetic energy.

The Heuristic Light-Quanta

These finding were in stark contradiction to classical predication and they puzzled physicist for many years. The world had to wait for the one and only Albert Einstein to solve the problem. In a 1905 article that was nothing short of luminary, he proposed an elegant solution that explained everything and a whole lot more.

 

He began by introducing somethings  called a "heuristic point of view" in other words, an informed guess. Just for the sake of argument, he supposed that a light ray was not spread continuously through space in the form of a wave, Rather, he suggested that it "consists of a finite number of energy quanta which are localized at points in space, which move can only be produced and absorbed as complete units." In other words, lights was composed of small, indivisible bundles that would eventually be called photons.

The Photons

The Photons is the fundamental quantum of electromagnetic radiation and can be thought of as a compact, localized bundle of light having a well-defined energy. Einstein hypothesized that the energy of a given light quanta was directly proportional to the light's frequency multiplied by Planck's constant: E=hf . Furthermore, if an electron absorbed a photon, all of the photon's energy was necessarily transferred to the electron. If these postulates held, he asked what would they imply for the photoelectric effect. 

The Photoelectric Effect

It is the ejection of electrons that occurs when electromagnetic radiation shines on a (typically metal)

surface. So what does his have to do with maxwell and his waves? First of all, Maxwell's equations tells us that the energy of a light wave has nothings to do with its frequency. Therefore, provided you shine your light brightly enough, you will always liberate electrons, you will always liberate electrons, no matter what frequency of light you happen to be using. Yet in the laboratory physicists saw that no electrons are ejected what so over when they used light that was at a frequency below a certain threshold. Moreover, if they increased the frequency of their light sources, the electrons that were ejected traveled faster and faster.

Maxwell's classical theory tells us that the energy of a light wave is determined by its intensity. This implies that the brighter you shine your light, the faster the liberated electrons should whiz through the lab. In reality, however , we find that the kinetic energy has no dependence whatsoever on the light's intensity. As scientists increased the brightness of their light sources, they simply produced more electrons with the same kinetic energy.

At the last, If we were to shine a  very sim light on the metal, maxwell's theory would tells us that you'd have to wait a littles while for the electrons to accumulate enough energy to break free of their atoms. His equations world even let we calculate just how long you'd have to wait. However, experiment proved that no such time lag existed, no matter how dimly physicists shined their light provided, that it was of high enough frequency.