Momentum Of Photon Formula

Photon is an important particle in quantum mechanics. Light and other such rays are made of photons. Albert Einstein was the first scientist to propose this concept. It heralded a new era in the world of physics.  So let us look into Momentum Of Photon Formula.

Photon

The photon is a type of elementary particle. Light is made up of photons. They are basically Qantas of energy. They have a mass of zero and travel with the speed of light in vacuum. Heisenberg’s uncertainty principle can be used to explain the behaviour of photons. This must be used because we are not aware of the momentum and the position of the photon simultaneously and accurately.

Momentum

The product of the mass and velocity of an object is its liner or translational or simply momentum. This is as per the Newtonian mechanics. It is a vector quantity, possessing a magnitude and a direction.

The object’s momentum is calculated as follows: p = m × v

where M = mass of the object and V = velocity of the object. In SI units, momentum is measured in kilogram meters per second (kg⋅m/s).

In any inertial frame, the linear momentum is conserved. The momentum of an object is calculated as per the second law of Newton which states that “the rate of change of momentum of a body is directly proportional to the force applied on it and is in that direction.”

Issac Newton one of the foremost scientist in humanity formed three laws of motion. These laws govern all the behaviour of the various object in the world. These laws are not applicable at the atomic level and therefore have to be modified before use in Quantum mechanics and Relativity. Heavenly bodies obey Newton’s laws of motions.

The Momentum of a Photon

The momentum of a photon is closely related to its energy. Just as the energy of a photon is proportionate to its frequency, the momentum of a photon is related to its wavelength. The momentum of a photon is given by the formula :

Consider the above diagram, it illustrates the “Compton Effect”. Arthur Compton discovered it and was awarded the Nobel Prize in Physics in 1929. The formula is :

p = h/λ

where,  p = momentum of the photon in Kg.m/s

h = Planck’s constant which has the value of 6.63×10−34 J ⋅ s

λ = wavelength of the wave carrying the photon in metres.

Since the value of the “h” is low the momentum of the photon is negligible in most of the cases. This is evident from the fact that the mirror doesn’t recoil when the photons bounce off it. Let us look into some sample problems to understand how the formula works.

Solved Example for Momentum Of Photon Formula

1.  Find the momentum of a photon of light in a beam of light with wavelength \(4 x 10^{-7}\) meters. Use Momentum Of Photon Formula

Answer: The formula is, p=h/λ

plugging in the values, p = 6.63×10−34 J ⋅ s \(4 x 10^{-7}\)

 =1.6575×10−27 kg⋅ m/s