Question

Let p and E denote the linear momentum and energy of a photon. If the wavelength is decreased,

Options

•  both p and E increase

• p increases and E decreases

• p decreases and E increases

•  both p and E decrease

Answer 1

both p and E increase

From the de-Broglie relation, wavelength,

`λ = h/p`       ....(1)

⇒ `p = h/λ`

Here, h = Planck's constant
             p = momentum of electron
It is clear from the above equation that `p ∝ 1/λ` .

Thus, if the wavelength `(λ)` is decreased, then momentum `(p)` will be increase .

Relation between momentum and energy :

`p = sqrt(2mE)`

Here, E = energy of electron
m = mass of electron
Substituting the value of p in equation (1), we get :

`λ = h/sqrt(2mE)` 

⇒ `sqrt(E) = h/(λsqrt(2m)`

⇒ `E = h^2/(2mλ^2`

Thus, on decreasing λ , the energy will increase .