Question

Which of the following is the correct set of four quantum numbers ($n$, $l$, $m$, $s$)?

• A. ( 3, 0, -1, +1/2)
• B. ( 4, 3, -2, -1/2)
• C. ( 3, 1, -2, -1/2 )
• D. ( 4, 2, -3, +1/2)

Answer 1

The Correct Option is B

A correct set of quantum numbers ($n$, $l$, $m$, $s$) must satisfy the following rules:

• Principal quantum number ($n$): $n = 1, 2, 3, \dots$
• Azimuthal quantum number ($l$): $l = 0, 1, 2, \dots, (n - 1)$
• Magnetic quantum number ($m$): $m = -l, \dots, 0, \dots, +l$
• Spin quantum number ($s$): $s = +\dfrac{1}{2}$ or $-\dfrac{1}{2}$

Let's check each option: 

(3, 0, -1, +1/2): Invalid because $m = -1$ is not allowed for $l = 0$ 
(4, 3, -2, -1/2): Valid
- $n = 4$
- $l = 3$ (allowed for $n = 4$)
- $m = -2$ (allowed for $l = 3$)
- $s = -1/2$ (allowed) 

(3, 1, -2, -1/2): Invalid because $m = -2$ is not allowed for $l = 1$ 
(4, 2, -3, +1/2): Invalid because $m = -3$ is not allowed for $l = 2$ 

Answer: (4, 3, -2, -1/2)