Question

The angular speed of electron in the nth orbit of hydrogen atom is 1. Directly proportional to n2 2. Directly proportional to n 3. Inversely proportional to n3 4. Inversely proportional to n

Answer 1

Answer:

inversely proportional to n3

Explanation:

angular speed = v/r

v=ke^2 m/ n h

r=ke^2 4pi^2 m^2 v^2 /m n^2 h^2

v/r is proportional to n^-3

Answer 2

Answer:

The correct option is 4. The angular speed of an electron in the nth orbit of a hydrogen atom is Inversely proportional to n.

Explanation:

We know, Linear speed is the product of angular speed and radius.

Mathematically it is expressed as, v = r × ω where v = linear speed, r = radius and ω = angular speed.

For, electron present in the nth orbit, the velocity becomes - v_n = r_n + ω_n

In terms of angular speed, the formula becomes- ω_n = v_n / r_n

We know, v_n = ze²/ 2ε₀nm

Therefore, equation becomes-

ω_n = ze²/ 2ε₀nm×r_n

Therefore, ω_n ∝ 1/n

Thus, the angular speed of an electron in the nth orbit of a hydrogen atom is inversely proportional to n.

#SPJ3