Understanding Light Quantization

[brajesh]

TL;DR

Understanding light quantization - energy distribution of a gas

Hi,

I'm still unclear on the quantization of light.

I watched this 1m video called "Why Light is Quantum" - Why Light is Quantum by minutephysics.

The author says light has the same energy distribution as a gas?
What does this mean?
What is an example of the energy distribution of a gas?

Perhaps by understanding the gas behavior, I will understand the light behavior too?

 

[Drakkith]

The author says light has the same energy distribution as a gas?

It means that if you plot the kinetic energy distribution of a large number of gas particles you get the same shape, with a gradual but increasingly steep rise from the low energy end to a peak with a sudden and exponentially decaying decline from the peak to the high energy end. Basically, most of the gas particles are moving within a certain range of kinetic energy, with few moving at extremely small or extremely high relative energies.

The light in a thermal spectrum (the type of spectrum emitted by a hot object like a light bulb filament) follows a similar pattern. Most of the light falls within a relatively small range of the spectrum, with very high and very low frequencies having very little light.

Consider the following. Let's say you add 100 joules of thermal energy to a gas of 10⁶ particles (one billion) that was very close to absolute zero. That 100 joules is distributed throughout the gas particles in such a way that most have 'middle' energies. Very few have energies anywhere close to 100 joules. You won't find that half the particles have 1 joule of energy each, as this would require 5x10⁵ joules, and we only have 100. In addition, the random nature of the particle collisions also prevents the energy being distributed in discrete amounts, meaning you won't find a gap or a jump in the graph.

On the lower end, it is statistically impossible for most of the gas particles to transfer their kinetic energy to a smaller number of gas particles through random collisions. This is why you won't find most of the gas particles at the lower end of the energy graph with a long trailing 'tail' towards the high energy end.

The spectrum of light follows a similar pattern because the underlying mechanism that creates the light is the random collisions of charged particles in the emitting material. Just like a gas, these charged particles follow a similar graph for their kinetic energy and so their various collisions cause them to emit a spectrum light that has a similar energy makeup.

In short, the energy of the emitted light depends on the energy of the colliding particles. There isn't enough energy to emit lots of high frequency light, but there is enough energy to make most of the emitting particles collide at moderate energies, not low energies.

 

[brajesh]

Thank you @Drakkith this is helpful.

 

[brajesh]

Is this an example of what you are describing?

Maxwell-Boltmann distribution

 

[PeterDonis]

Is this an example of what you are describing?

Maxwell-Boltmann distribution

It is, but only for a gas of classical particles. The correct distribution for light would be the Bose-Einstein distribution.