# Eli5 to me the energy of a single photon

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Hello It Is not clear to me how would be possible to calculate the energy possessed by a single photon or if you prefer how do one calculate the wave lenght of a single photon?
To my knowledge (since mass and speed are constant in photons right?) The energy of a photon depends only on it’s frequency (or the wave lenght of course) but I Just don’t understand how the frequency of a single photon can be calculated? Or how the wavelenght info can be extracted from a single wave (in this case electromagnetic wave)?

In: 1 Photons do not have mass in the traditional sense like we are used to, that is the rest mass that objects that do not move have. The rest mass of photons is zero.

The speed of photons is constant or more exactly constant in a vacuumm , that is c.

Energy is equivalent to mass, the famous formula E=mc^2 shows the connection between mass and energy. In relativity, the relativistic mass is the rest mass and mass that is added because of energy.

Photons only have relativistic mass and it is not constant

E=mc^2 is not the complete formula, it on only valid for objects that do not move The complete formula is E^2 = =(pc)^2 + (m0c^2)^2 where p is the momentum and m0 is the rest mass.

The rest mass m0 of a photon is zero so only the formula E^2 =(pc)^2 => E= pc

Photons have momentum and move at a constant speed but have no rest mass.

The relationship between energy and frequency is

E= hf where h is Planck constant and it is the frequency

Because frequency = sped/ wavelength you can also use.

E=hc/λ where λ is the wavelength.

You can use it with E= pc => p=E/c and get

p=E/c =(hc/λ)/c)=h/λ

To calculate one you can just plug in the known value you have and calculate the other.

If you talk about measuring the energy of a single photon there there are ways. The angle of visible light bends when it changes medium depending on the wavelength, this is why rainbow and prism split up light. Let the split light then hit a sensor, the location is dependent on the wavelength. So we can measure the weight of a single photon but notice where it hits the sensor.

An instrument that do this is called a https://en.wikipedia.org/wiki/Spectrometer First of all, you are correct, the energy of a photon depends entirely on its wavelength and vice versa. So the question is, how do we determine one of those for a single photon.

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Let’s say we want to approach this via the energy. There is a phenomenon called the photoelectric effect, where a single photon hits an electron in an atom and, if it has enough energy, knocks it out of the atoms shell.

We can now measure the energy of that electron by applying an electric field, and if we know how much energy it takes to knock the electron out of the atom in the first place we can easily determine the energy of the photon and therefore the wavelength.

This is an indirect approach, but it is the best I can think of right now where a single photon is responsible for the effect. (Note that measuring a single electron is really hard, and the photon may or may not hit one anyway, so you would usually shoot a lot of photons and measure a lot of electrons.

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If you want to measure the wavelength directly, you can use something called an Interferometer, where you get a beam of photons, all of the same wavelength, split that beam to send it on two different paths and reconnect them again.

This is a bit tricky to explain without pictures, but you can vary one of the lengths of the paths and see, how the recombined beam goes darker and lighter again, and the difference in length corresponds to the wavelength.

This is a more direct approach to measuring the wavelength but it isn’t really a single photon.