Question

Part B

In what length rigid box will an electron undergoing a 2?1 transition emit light with a wavelength of 534 nm ?

Express your answer with the appropriate units.

Answer 1

When an electron makes an transition from 2nd orbit to 1st orbit, the energy is calculated as

E₂ - E₁ = 2.18 x 10^-18 [ (1 / n_{i^{2) - (}}1 / n_f²)] J.

Substituting for n_i = 2 and n_f = 1, we get E₂ - E₁ = - 16.35 x 10 ^-19 J

The value of energy of a particle in a rigid box for n^th orbit is given by

where n is the orbit number, h is Planck's constant, m is the mass of the electron, L is the lenght of the rigid box and E_n is the energy of the particle in n^th orbit.

Here E_n = E₁ - E₂ = .

E₁ - E₂ = h² ( - 4 + 1) / 8 m L²  

Thus  L² = 0.1106 X 10^-18 m²

L = 0.332 X 10^-9 m.

L = 0.332 nm.