For ground level: n₁ =4

Energy for the ground level of hydrogen atom, E₁ = -13.6/n₁²

Substituting the value, we get

E₁ = -13.6/1² = -13.6 eV

When the hydrogen atom is excited to n₂= 4, then the energy absorbed by the photon is given as:

E₂ = -13.6/4²

E₂= -13.6/16

The energy absorbed by the photon can be calculated by the following:

E = E₂- E₁

Or, E = (-13.6/16)- (-13.6/1)

On calculating, we get

E = 12.75 eV

In Joules, Energy is = 12.75 × 1.6 × 10^-19 Joules

Or E = 2.04 × 10^-18 J

Energy is given by the relation, E =hc/λ

Or λ = hc/E

Where h is Planck’s constant and is equal to 6.64 × 10^-34 Js

c is speed of light and is equal to 3.0 × 10⁸ m/s

substituting the values we get

On calculating, we get

λ = 9.7 × 10^-8 m

or λ = 97 nm

Frequency can be calculated as follows:

v = c/λ

substituting the values, we get

v= 3.1 × 10¹⁵ Hz