Question

What is the angular momentum of an electron in the ground state of a hydrogen atomand by how much does that angular momentum increase when the electron moves to thenext higher energy level?

Answer 1

In the nth orbit of the hydrogen atom, the angular momentum of the electron is mentioned as, Ln = nh/2π

In the case of the ground state, n = 1, thus, the angular momentum of the electron in the ground state will be,

L1 = 1 h/2π

= (1) (6.626 × 10⁻³⁴J.s)/2π × (1kg.m².s⁻²/1J)

= 1.055 × 10⁻³⁴ kg. m²/s

For the first excited state or the next higher energy level, n = 2. Thus, the angular momentum of electron in ground state will be,

L2 = (2) h/2π

= (2) (6.626 × 10⁻³⁴ J.s) / 2π × (1kg.m².s⁻²/1J)

= 2.11 × 10⁻³⁴ kg. m²/s

Now, the increase in angular momentum is as follows:

L2-L1 = (2.11 × 10⁻³⁴ kg. m²/s) - ( 1.055 × 10⁻³⁴ kg. m²/s)

= 1.055 × 10⁻³⁴ kg.m²/s