Question

1. (a) What is the angular momentum of an electron in the ground state of a hydrogen atom and by how much does that angular momentum increase when the electron moves to the next higher energy level?

2. (b) Provide a concise explanation for how the answers to the previous questions can be explained in terms of resonance and the de Broglie hypothesis that electrons have a wavelength that is inversely proportional to their momentum.

Answer 1

(a)

Concept Used :

According to Bohr postulates,

Electrons can revolve only in those orbits for which the angular momentum is some integral multiple of nh/2.

where,

h = Planck's constant = 6.62607004 × 10-34 m2 kg /s

n = principal quantum number 1,2,3......

Formula Used :

angular momentum,

Solution :

Step-1 : To find Angular momentum of an electron in the ground state ( n = 1 ) of a hydrogen atom

     (ANSWER)

Step-2 : To find Angular momentum increase when the electron moves to the next higher energy level i.e. from n=1 to n=2

Using above formula of Angular momentum, we get,

    (ANSWER)