# Momentum of Photon Formula

• Last Updated : 27 Apr, 2022

A photon is a positively charged particle with zero mass that travels at the speed of light in a vacuum. The momentum of a photon is defined as the strength or energy gained by it while it is in motion. It is equal to the product of mass and velocity of the photon and is denoted by the symbol p. It is a vector quantity, i.e., it has both magnitudes as well as direction. Its unit of measurement is kilogram meters per second (kg m/s).

Formula

p = h/λ

where,

p is the photon momentum,

h is the Planck’s constant with a value of 6.63 × 10−34 Js,

λ is the wavelength of the photon carrying wave.

Derivation

Suppose there is a photon of mass m that travels with the speed of light, that is, c.

The momentum of this photon is given by the formula,

p = mc    ……. (1)

Now the energy of the photon is given by,

E = mc2    ……. (2)

E = hv

Putting v = c/λ in the equation, we get

E = hc/λ

Using (2) in LHS of the above equation we have,

hc/λ = mc2

m = h/λc    ……. (3)

Putting (3) in (1) we get,

p = (h/λc) c

p = h/λ

This derives the formula for momentum of the photon.

### Sample Problems

Problem 1. Calculate the momentum of a photon with a wavelength of 2 x 10−5 meters.

Solution:

We have,

h = 6.63 × 10−34

λ = 2 x 10−5

Using the formula for momentum of photon we get,

p = h/λ

= (6.63 × 10−34)/(2 x 10−5)

= 3.31 x 10−29 kg m/s

Problem 2. Calculate the momentum of a photon with a wavelength of 6 x 10−3 meters.

Solution:

We have,

h = 6.63 × 10−34

λ = 6 x 10-3

Using the formula for momentum of photon we get,

p = h/λ

= (6.63 × 10−34)/(6 x 10−3)

= 1.10 x 10−31 kg m/s

Problem 3. Calculate the momentum of a photon with a wavelength of 2.76 x 10-7 meters.

Solution:

We have,

h = 6.63 × 10−34

λ = 2.76 x 10-7

Using the formula for momentum of photon we get,

p = h/λ

= (6.63 × 10−34)/(2.76 x 10−7)

= 2.40 x 10−27 kg m/s

Problem 4. Calculate the momentum of a photon with a wavelength of 5.15 x 10-4 meters.

Solution:

We have,

h = 6.63 × 10−34

λ = 5.15 x 10-4

Using the formula for momentum of photon we get,

p = h/λ

= (6.63 × 10−34)/(5.15 x 10−4)

= 1.28 x 10-30 kg m/s

Problem 5. Calculate the wavelength of a photon with a momentum of 2.71 x 10-24 kg m/s.

Solution:

We have,

h = 6.63 × 10−34

p = 2.71 x 10-24

Using the formula for momentum of photon we get,

p = h/λ

=> λ = h/p

=> λ = (6.63 × 10−34)/(2.71 x 10-24)

=> λ = 2.44 × 10−10 m

Problem 6. Calculate the wavelength of a photon with a momentum of 4.61 x 10-31 kg m/s.

Solution:

We have,

h = 6.63 × 10−34

p = 4.61 x 10-31

Using the formula for momentum of photon we get,

p = h/λ

=> λ = h/p

=> λ = (6.63 × 10−34)/(4.61 x 10-31)

=> λ = 1.43 × 10−3 m

Problem 7. Calculate the wavelength of a photon with a momentum of 3.83 x 10-29 kg m/s.

Solution:

We have,

h = 6.63 × 10−34

p = 3.83 x 10-29

Using the formula for momentum of photon we get,

p = h/λ

=> λ = h/p

=> λ = (6.63 × 10−34)/(3.83 x 10-29)

=> λ = 1.73 × 10−5 m

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