Quantum Mechanics Made Simple: A Beginner’s Guide to the Quantum World

The Origin and Evolution of Quantum Mechanics

Quantization Of Energy

“There is nothing new to be discovered in physics now. All that remains is more and more precise measurement.” This sentence was pronounced by a famous Scottish physicist William Thomson on the verge of the 20th century, and many contemporary physicists undoubtedly agreed with him. Classical physical theories had been tested many times and seemed to describe reality tolerably. Not until later, when these theories started to fall apart, did come to light how horribly wrong Thomson was. The first phenomenon which classical physics failed to explain is called the black-body radiation.

To understand this phenomenon, it is necessary to know that all tangible bodies in the universe emit energy in the form of electromagnetic radiation (light). The amount of energy emitted by a body depends on several factors, such as temperature or color of the body. The higher the temperature of a body, the higher the average frequency (and thereby energy) of the light it emits. The reason we usually cannot observe this radiation is that bodies at room temperature emit predominantly light from the infrared spectrum, which is not visible to the naked eye. Visible light is emitted by metals during melting, for example, when their temperature reaches several hundreds of degrees Celsius, making it possible for us to see them glow.

Physicists of the 19th century were trying to ascertain the spectral composition emitted by a body in relation to its temperature. To accomplish that, they used a simplified model of a body – the black body. A black body is a hypothetical body that has to meet the following two conditions:

1. A black body absorbs all the electromagnetic radiation that strikes it (other bodies absorb merely a certain part of the whole spectrum and reflects the remaining light).

2. A black body stays in thermal equilibrium with its surroundings (i.e., has the same temperature as all the bodies located within the same system).  

These conditions ensure that spectrum emitted by a black body is determined purely by the temperature of the body. However, when physicists tried to establish the composition of such a spectrum using classical physics, they obtained a result that did not coincide with reality whatsoever. According to classical physics, a black body would emit the same amount of light of each frequency. However, the higher the light’s frequency, the more energy the light has. A black body would therefore emit huge quantities of energy in the form of high-frequency radiation – infinite, in fact. 

This, however, has dire consequences – classical physics thereby basically states that every single object in the universe should immediately emit all of its energy in the form of light from the ultraviolet spectrum. Luckily, the universe does not work that way, otherwise we would not exist. This realization was a huge milestone for the evolution of modern science. Physicists were at last unwillingly forced to admit that classical theories were simply wrong. Today, we have an apt name for this huge failure of classical physics – the ultraviolet catastrophe.

quantum mechanics

The black-body radiation problem was solved by a German physicist Max Planck. He came up with an idea that bodies do not emit electromagnetic radiation continuously, but via small packets called quanta. The size of these quanta is given by the following Planck’s equation: 

E=hf(h=6.626 × 10-34)

Electromagnetic wave can essentially be thought of as a set of very small energy “packets” (quanta) whose total energy determines the energy of the wave itself. The size of a quantum is specific for each frequency. From the equation above, it is apparent that radiation of higher frequencies is composed of larger quanta than radiation of lower frequencies. This solves the problem with black-body radiation – it is increasingly difficult for a black body to emit radiation of higher frequencies, as it often cannot “feed” high-frequency quanta with enough energy, and thus sticks with low-energy light.

Quantization of energy is just the very beginning of a whole new world of physics. It presents a fundamental rule to quantum mechanics – as we will learn in the following chapters.

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