Question

The ratio of orbital angular momentum of electron having l = 1 and l = 4 respectively will be
(1)=1:3
(2)=√2:1
(3)=1:√10
(4)=2:√5

Answer 1

Given:

An electron with two l values 1,4 respectively.

To Find:

The ratio of orbital angular momentum of the electron.

Solution:

1. The l values of the electron are 1,4.

(l is the notation of azimuthal quantum number which is also referred as to angular momentum quantum number).

2. The values of l primaririly depends upon the principal quantum number which is denoted by n. ( n=l-1 is the relation between n and l)

3. Orbital angular momentum of an electron with azimuthal value l is given by  $\sqrt{l(l+1)}$*(h/2*3.14). (Here 3.14 refers to the aproximate value of π).

Where, h is Planck's constant, l is the azimuthal quantum number.

4. The ratio of orbital angular momentum can be found by substituting the values of l in the given formula i.e,

=> Ratio of orbital angular momentum =$\sqrt{2/20} }$.

• (Since Planck's constant(h) is a constant and it gets cancelled in both the numerator and the denominator).

=>Ratio of angular momentum =$\sqrt{1/10}$.(which is also equal to 1: $\sqrt{10}$.

Therefore the ratio of orbital angular momentum of the electron with l value 1 and 4 is 1:√10.