Question

Angular momentum for p-shell electron is:
  (A) $\dfrac{3h}{\pi }$
  (B) Zero
  (C) $\dfrac{\sqrt{2}h}{2\pi }$
  (D) None of these

Answer 1

Hint: We are asked to find the angular momentum for a p-shell electron. It can be found by using a formula which involves the Azimuthal quantum number. For a p shell electron, the value of Azimuthal quantum number will be one. Thus, by substituting it in the formula we get the angular momentum.

Complete step by step answer:
  - As we know, orbital angular momentum is the analogue of angular momentum in classical mechanics. There are four quantum numbers and they are Principal quantum number, Azimuthal quantum number, Magnetic quantum number and Spin quantum number.
 - Orbital angular momentum is associated with the Azimuthal quantum number. It describes the shape of the orbital also. It is usually represented as $l$
 - The value of Azimuthal quantum number ($l$ ) varies from zero to n−1, where n is the principal quantum number. Thus, for a p orbital the value of $l$ will be 1.
 - The equation for finding orbital angular momentum (L) can be written as follows
  $L=\dfrac{\sqrt{l\left( l+1 \right)}h}{2\pi }$

 Where $l$ is the Azimuthal quantum number
              h is the Planck's constant

  - In the given question we are asked to find the orbital angular momentum for a p shell electron. As we mentioned above, for a p electron the value of Azimuthal quantum number is given as. Let's substitute this in the above equation for finding the orbital angular momentum. Thus, the equation becomes
$L=\dfrac{\sqrt{1\left( 1+1 \right)}h}{2\pi }$
     =$\dfrac{\sqrt{2}h}{2\pi }$

Therefore, the answer is option (C). That is, the orbital angular momentum for a p shell electron is $\dfrac{\sqrt{2}h}{2\pi }$.
So, the correct answer is “Option C”.

Note: It should be noted that each value of the azimuthal quantum number corresponds to a subshell. If the $l$ =0, then it represents an s subshell and it will have a spherical shape. It has only one orbital, s orbital. As we mentioned if $l$ =1 then it represents a p subshell and it will have three dumbbell-shaped orbitals: The azimuthal quantum number $l$ =2 represents a d subshell. And thus, it will have 4 dumbbell-shaped orbitals and 1 doughnut-shaped orbital. Similarly, if $l$ =3 it would be an f subshell, and will have 7 orbitals.