Question

Determine the end (final) value of n in a hydrogen atom transition, if the electron starts in n = 2 and the atom absorbs a photon of light with a frequency of 4.57 × 10 14 Hz. (This question has already been posted, however, the answers for it dont match the options).

Answer 1

We know that frequency , v = c / λ

Where

c = speed of light = 3x 10⁸m/s

λ = wave length = ?

v = Freqency = 4.57x10¹⁴ Hz

Plug the values we get λ = c / v = 6.564x10^-7 m

Also From Rydburg's Equation , 1/ λ = R[(1/n_i²) – (1/n_f²)]

   Where R = Rydburg's constant = 10.96 x10⁶ m^-1
               λ = wavelength = 6.564x10^-7 m
               n_i = 2
               n_f = ?
Plug the values we get [(1/n_i²) – (1/n_f²)] = 1 / (λ R) = 0.139

[(1/2²) – (1/n_f²)] = 0.139

   (1/n_f²) = 0.111

  n_f²=9

n_f = 3