Question

Draw a neat and labelled energy level diagram and explain Balmer series and Brackett series of spectral lines for hydrogen atom. The work function for a metal surface is 2.2eV. If light of wavelength 5000Å is incident on the surface of the metal, find the threshold frequency and incident frequency. Will there be an emission of photoelectrons or not ?

(c = 3 × 10⁸ m/s, 1 eV= 1.6 × 10^–19 J, h = 6.63 × 10^–34 J.s.)

Answer 1

The Balmer series of the radiation corresponds to n_i= 2 and n₀ = 3, 4, 5 .......... The wavelength is given by

They lie in the visible region.

The Brackett series of the radiation corresponds to n₁ = 4 and n₀ = 5, 6, 7 ........... The wavelength of radiations is given by

They lie in the far infrared region.

Emission of photoelectron takes place only if incident frequency is greater than the threshold frequency. But, in this case n > n₀, therefore, photoelectric emission takes place.