Question

A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of the photon.

Answer 1

For ground level, n₁ = 1

Let E₁ be the energy of this level. It is known that E₁ is related with n₁ as:

The atom is excited to a higher level, n₂ = 4.

Let E₂ be the energy of this level.

The amount of energy absorbed by the photon is given as:

E = E₂ − E₁

For a photon of wavelengthλ, the expression of energy is written as:

Where,

h = Planck’s constant = 6.6 × 10⁻³⁴ Js

c = Speed of light = 3 × 10⁸ m/s

And, frequency of a photon is given by the relation,

Hence, the wavelength of the photon is 97 nm while the frequency is 3.1 × 10¹⁵ Hz.