Question

The orbital angular momentum of a p-electron is given as:
(a) \[\sqrt{3}\dfrac{h}{2\pi }\]
(b) \[\sqrt{\dfrac{3}{2}}\dfrac{h}{\pi }\]
(c) \[\sqrt{6}.\sqrt{\dfrac{h}{2\pi }}\]
(d) \[\dfrac{h}{\sqrt{2}\pi }\]

Answer 1

Hint: Bohr’s atomic model states many postulates for the arrangement of electrons in different orbits around the nucleus. According to one of his postulates, an electron can move around the nucleus in that circular orbital for which its angular momentum is an integral multiple of \[\dfrac{h}{2\pi }\].

Complete step by step answer:
According to the question, we need to find the angular momentum of a p-electron, i.e., this electron belongs to the p-orbital.
As we know, orbital angular momentum depends on ‘l’.
For p-orbital, the value of l = 1.
Formula of orbital angular momentum (m) is give as –
Orbital angular momentum = \[\sqrt{l(l+1)}\dfrac{h}{2\pi }\]
Since, l = 1.
Therefore,
Orbital angular momentum (m) = \[\sqrt{1(1+1)}\dfrac{h}{2\pi }\] = \[\sqrt{2}\dfrac{h}{2\pi }\]
On rationalization (i.e. multiplying numerator and denominator by\[\sqrt{2}\]), we get –
m =\[\dfrac{\sqrt{2}h}{2\pi }\times\dfrac{\sqrt{2}}{\sqrt{2}}\]
 m =\[\dfrac{h}{\sqrt{2}\pi }\].
Therefore, the answer is – option (d) – The orbital angular momentum of a p-electron is given as \[\dfrac{h}{\sqrt{2}\pi }\].

Additional Information: The value of ‘l’ for different orbitals is as follows –
l = 0 for s-orbital
l = 1 for p-orbital
l = 2 for d-orbital
l = 3 for f-orbital

Note: The quantum number represents the complete address of an electron. There are four types of quantum numbers –
1. Principal quantum number (n)
- It tells about the size of the orbital, i.e. the average distance of an electron from the nucleus.
2. Azimuthal quantum number (l)
- It denotes the sub-level (orbital) to which the electron belongs.
- It ranges from 0 to (n-1).
3. Magnetic quantum number (m)
- It determines the preferred orientation of orbitals in space
- For each value of l, there are 2l+1 values of m.
4. Spin quantum number (s)
It tells about the direction of spin.
+1/2 represents clockwise spin.
-1/2 represents anti-clockwise spin.