Question

A hydrogen atom is in the ground state. It absorbs energy and makes a transition to the n = 5 excited state. The atom returns to the ground state by emitting two photons, one in dropping to n = 4 state, and one in further dropping to the ground state. What are the photon wavelengths of (a) the first and (b) the second transitions?

Answer 1

a )

using the formula wavelength is

1 / = R ( 1 / n_f²- 1 / n_i² )

1 / = 1.097 X10^7 ( 1 / n_f²- 1 / n_i² )

with iven data n = 5

and n = 4

1 / = 1.097 X10^7 ( 1 / 4²- 1 / 5² )

1 / = 1.097X10^7 ( 1 / 16- 1 / 25)

1 / = 246825

= 4051.45 nm

b)

1 / = R ( 1 / n_f²- 1 / n_i² )

1 / = 1.097X10^7 ( 1 / n_f²- 1 / n_i² )

with iven data n = 4

and n = 1

1 / = 1.097 X10^7 ( 1 / 1²- 1 / 4² )

1 / = 10284375

= 1 / 10284375

then finally

= 97.23 nm