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Q & A: Why the number of photons decreases with energy?

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Most recent answer: 05/12/2015
Q:
Could someone please explain to me why the number of photons decreases with the increase of its energy and is that proved experimentally?
- Radwan (age 18)
Egypt
A:

In case the system of concern has a constant power output, less photons should be emitted with high energy per photon, so that the total product (numebr of photons times energy per photon) is constant. 

In case you are interested in natural radiation phenomon, your statement is not strictly true. There is a bell-shaped distribution of photons with respect to energy (see ). The photon count per enrgy range only decreases after a peak energy value. Experimental emission spectra  agree with that. But there is one easy evidence for it: since energy spectrum is unbounded at the high end, a non-decreasing spectrum would give an infinite area beneath it, which would mean an infinite brightness. But this is not the case: we are not immediately blinded.

The radiation of photons is only possible between certain energy levels, the transitions from high to low energy states result in photon emission with an energy equal to this gap. But this certainly requires that the high energy state should be occupied. The occupancy level is determined by the Boltzmann factor (), which says that there will be a general preference against high energy states. Since high energy states have lower occupancy, there will also be less emissions with high energy.

Tunc

Generally, in thermal equilibrium high energy states are less likely to be occupied than low energy states. That was figured out by Boltzmann. The reason is that the less energy taken up by one part, the more energy is available for other parts to reach other states. And thermal equilibrium is reached by exploring as many states as possible. That argument applies to photon states as well as any other states. The distribution of numbers of what we now call photons of different energies at some temperature was worked out by Planck in 1900, starting the quantum mechanical revolution. /mw


(published on 05/12/2015)

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