Question

The angular momentum of an electron in a hydrogen atom is proportional to (where r is radius of orbit ):

a) 1/r1/2
b) 1/r
c) r1/2
d) r2

Answer 1

Radius of the nth orbit rn ∝ n2/Z      ⇒    n ∝ (rn)½ Angular momentum Ln = nh/(2π) ∝ (rn)½ So the answer is (c).

Answer 2

Answer: The correct answer is (a).

Explanation:

1. The radius of the orbit is directly proportional to the $\frac{n^{2}}{Z}$.

Here, Z is the atomic number and n is the quantum number.

The expression for the angular momentum of an electron in a hydrogen atom is as follows;

$L=\frac{nh}{2\pi }$

Here, h is Planck's constant.

It can be concluded from the point 1 that the angular momentum of an electron in a hydrogen atom is directly proportional to the square root of the radius of the orbit.

Therefore, the correct option is (a).