Question

What are the values of the quantum numbers associated with the following orbitals: 2p, 3s, and 5d?

Answer 1

Hint: An atomic subshell is represented by a principal quantum number, followed by corresponding letter notation for the angular momentum quantum number. The magnetic quantum number can always have possible values from -l to +l. A spin quantum number can always have the value of $-\dfrac{1}{2}$ or $+\dfrac{1}{2}$.

Complete answer:
Each electron in an atom can be described by four different quantum numbers: $\text{n , l , }{{\text{m}}_{\text{l}}}\text{ , }{{\text{m}}_{\text{s}}}$. Let us understand what these quantum numbers denote.
(1) Principal Quantum Number (n): It specifies the energy and size of the orbital. The lowest possible value of n is 1. The orbitals having the same value of n are said to be in the same shell. For example, the orbitals written as 2s and 2p belong to the same shell and their principal quantum number is 2.
(2) Angular or Azimuthal quantum number (l): This quantum number identifies the shape of an atomic orbital having a certain value of “n” (principal quantum number). It divides the shell into subshells and is represented by letters: s,p,d, and f. Its value ranges from $0-\left( \text{n-1} \right)$.

SUBSHELL	AZIMUTHAL QUANTUM NUMBER (l)
s	0
p	1
d	2
f	3

(3) Magnetic quantum number $\left( {{\text{m}}_{\text{l}}} \right)$: It specifies the spatial orientation of orbitals of given energy (n) and shape (l). This further divides the subshell into orbitals. There are $\left( 2\text{l}+1 \right)$ orbitals in each subshell.

AZIMUTHAL QUANTUM NUMBER (l)	MAGNETIC QUANTUM NUMBER $\left( {{\text{m}}_{\text{l}}} \right)$
0	0
1	-1, 0, +1
2...l	-2, -1, 0, +1, +2...-l to +l

(4) Spin Quantum number $\left( {{\text{m}}_{\text{s}}} \right)$ : It tells about the spin orientation of an electron. An electron can only have one of two spins. It can be either upward or downward and written as $-\dfrac{1}{2}$ and $+\dfrac{1}{2}$ .
Hence, the quantum numbers associated with the following orbitals are:

ORBITAL	PRINCIPAL QUANTUM NUMBER (n)	AZIMUTHAL QUANTUM NUMBER (l)	MAGNETIC QUANTUM NUMBER $\left( {{\text{m}}_{\text{l}}} \right)$	SPIN QUANTUM NUMBER $\left( {{\text{m}}_{\text{s}}} \right)$
2p	2	1	{-1, 0, +1}	$-\dfrac{1}{2}$ or $+\dfrac{1}{2}$
3s	3	0	{0}	$-\dfrac{1}{2}$ or $+\dfrac{1}{2}$
5d	5	2	{-2, -1, 0, +1, +2}	$-\dfrac{1}{2}$ or $+\dfrac{1}{2}$

Note:
When an electron spins, it creates a magnetic field, which can be oriented in one of two directions. For two electrons in the same orbital, the spins must be opposite to each other. The atoms in which all electrons are paired up with opposite spins are said to be diamagnetic. Atoms with more electrons that spin in one direction than another unpaired electron are said to be paramagnetic.