# Photon Number, Energy, and Wavelength

*Most recent answer: 05/06/2012*

- Gehad (age 18)

Egypt

Your premise about the number of photons and energy is not quite correct. The relation that we now believe to be correct is that the wavelength of the photon decreases as the energy of the photon increases. They are related by λ = hc/ E

_{photon}where h is Plank's constant, c is the velocity of light and λ is the wavelength of the photon.

In a given packet of photons the total energy is proportional to the number of photons.

LeeH

*(published on 05/06/2012)*

## Follow-Up #1: More on energy and photon number.

- Gehad (age 18)

Egypt

The first statement is correct. The only way the second statement is correct is if the writer implied that "For a constant amount of total energy, the number of photons would decrease as the frequency increases". Otherwise it's wrong as explained in the previous post.

LeeH

*(published on 05/07/2012)*

## Follow-Up #2: why is photon energy hf?

- hajra naeem (age 18)

hadali

The number of photons is just the energy divided by the energy per photon. So why is the energy E of a photon proportional to its frequency, f,: E=hf? That's a deep question.

It leads straight to a deeper question: the energy of *anything* is just hf where h is Planck's constant and f is the frequency at which the quantum state changes phase. Like some very deep questions, the answer is almost trivial. If E=hf, *always*, then E and f are just the same thing, expressed in different units. Planck's constant is just the conversion factor from conventional frequency units to conventional energy units.

Now we get to the real physics. Why is the quantum f from that universal definition, E-hf, the same as the frequency you get from measuring the oscillation of the electric field in a wave made of photons? This is subtle. The electric field for any single photon has an expected value of zero. Electric field oscillations come from beats between states with different numbers of photons, differing by one. So the beat frequencies are just f, the single-photon quantum frequency. Really, we don't expect that this short last argument should be very clear. Usually it isn't learned until one takes a graduate quantum mechanics course.

Mike W.

*(published on 02/12/2015)*