Question

Which of the following sets of quantum numbers represent an impossible arrangement :-

• A. n = 3, l = 2, m = -2, $m_s$ = $\frac{1}{2}$
• B. n = 4, l = 0, m = 0, $m_s$ = $\frac{1}{2}$
• C. n = 3, l = 2, m = -3, $m_s$ = $\frac{1}{2}$
• D. n = 5, l = 3, m = 0, $m_s$ = $\frac{1}{2}$

Answer 1

Answer: (C)

The set with n = 3, l = 2, and m = -3 is impossible because for l = 2, m can only range from -2 to +2.

Answer 2

The rules for quantum numbers are:

1. Principal quantum number (n): Can be any positive integer (1, 2, 3, ...).
2. Azimuthal quantum number (l): Can range from 0 to (n-1).
3. Magnetic quantum number (m_l): Can range from -l to +l, including 0.
4. Spin quantum number (m_s): Can be +1/2 or -1/2.

In option (C), for l = 2, m_l can only be -2, -1, 0, 1, 2. Therefore, m_l = -3 is not allowed.