# Momentum of photon proof

• Kehsibashok
In summary, the conversation discusses the concept of momentum for photons, which have no rest mass. The equation p = mv is only applicable for massive particles at low speeds, while for photons, their momentum is determined by the energy they can impart to a mechanical system. The de Broglie relation, p=h/lambda, is derived from the Planck relation and is experimentally proven through diffraction patterns. For further understanding, it is encouraged to study electromagnetic field theory.

#### Kehsibashok

1.photon has no mass . so m=0.hence, p=mv=0.by doing some calculations , we can get that
p=h/lambda.we can prove p=mv experimentally.but how can we prove the second one experimentally?

Kehsibashok said:
1.photon has no mass . so m=0.hence, p=mv=0.by doing some calculations , we can get that
p=h/lambda.we can prove p=mv experimentally.but how can we prove the second one experimentally?
p = mv is only useful for massive particles at relatively low speeds. For photons, you'll need the relativistic energy-momentum relation: Energy–momentum relation

There is more than one type of momentum - p=mv is the mechanical form.

Momentum for electromagnetic radiation is determined by the momentum that it can impart to a mechanical system. The derivation follows from energy transport properties of radiation derived from Maxwell's equations - look up "Poynting Vector". The electromagnetic radiation momentum is found to be p=E/c; this relation also holds for the photon.

The equation p=h/lambda is the de Broglie relation; it is "derived" from the Planck relation (E=h*f), then divide by c to get E/c=p=h*f/c=h/lambda. Of course this is not a derivation - it merely shows that the two are algebraicly consistent. The experimental proof of the de Broglie relation can be seen experimentally: x-rays and electrons both give diffraction patterns in accordance with the above.

For more detail see http://hyperphysics.phy-astr.gsu.edu/hbase/debrog.html

only rest mass of photon is zero

momentum of photon can be calculated by

p = E/c

where E is energy of photon
don't ask me any proof please because I'm an tenthee! studying for iit and was told this on a chemistry lecture and would study more on it guess in my research later
further proofs are encouraged and needed by me as my teacher said it would come later on:tongue:

and a kind request to UltrafastPED pls do no\umerically in separate lines or it's feels scrambled

"and a kind request to UltrafastPED pls do no\umerically in separate lines or it's feels scrambled"

I prefer inline formulas, especially when there are chains of implication. This makes for more concise, "unscrambled" chains of logic.

BTW, for the proof of p=E/c see any text on electromagnetic field theory (upper level undergraduate physics); you will arrive at the Poynting vector sometime in the second semester!

## 1. What is the momentum of a photon?

The momentum of a photon is given by the formula p = E/c, where E is the energy of the photon and c is the speed of light. This means that photons have momentum because they have energy and travel at the speed of light.

## 2. How is the momentum of a photon calculated?

The momentum of a photon can be calculated using the formula p = E/c, where E is the energy of the photon and c is the speed of light. This calculation is based on the fact that photons have energy and travel at the speed of light.

## 3. Does a photon always have momentum?

Yes, a photon always has momentum because it has energy and travels at the speed of light. According to the laws of physics, any object with energy and speed must have momentum.

## 4. Can the momentum of a photon be changed?

Yes, the momentum of a photon can be changed by changing its energy or direction of travel. This can happen through interactions with other particles or objects, such as when a photon is absorbed or reflected off a surface. However, the speed of light is constant, so the magnitude of the change in momentum will always be equal to the change in energy.

## 5. What is the significance of the momentum of a photon?

The momentum of a photon is significant because it helps us understand the behavior of light and other electromagnetic radiation. It also plays a role in various phenomena, such as the photoelectric effect and the Compton effect, which have important implications in fields like quantum mechanics and atomic physics.