Question

The INCORRECT combination of quantum numbers amongst the following is:

• A. \( n = 1, \, l = 0, \, m_l = 0, \, m_s = -\frac{1}{2} \)
• B. \( n = 1, \, l = 1, \, m_l = 0, \, m_s = +\frac{1}{2} \)
• C. \( n = 2, \, l = 1, \, m_l = +1, \, m_s = -\frac{1}{2} \)
• D. \( n = 3, \, l = 1, \, m_l = 0, \, m_s = +\frac{1}{2} \)

Hint:

In quantum mechanics, pay close attention to the allowed values of quantum numbers. For \( n = 1 \), \( l = 0 \) is the only possible value, which makes (B) an incorrect combination.

Answer 1

The Correct Option is B

Quantum numbers describe the state of an electron in an atom. They must satisfy the following restrictions:
1. \( n \) (the principal quantum number) must be a positive integer (\( n = 1, 2, 3, \dots \)).
2. \( l \) (the angular momentum quantum number) can take integer values from \( 0 \) to \( n-1 \), i.e., \( l = 0, 1, 2, \dots, n-1 \).
3. \( m_l \) (the magnetic quantum number) can take integer values from \( -l \) to \( +l \), i.e., \( m_l = -l, -l+1, \dots, l-1, l \).
4. \( m_s \) (the spin quantum number) can take values \( +\frac{1}{2} \) or \( -\frac{1}{2} \).
Now, checking the given combinations:
- (A) is correct because \( n = 1, l = 0, m_l = 0, m_s = -\frac{1}{2} \) is allowed.
- (B) is incorrect because for \( n = 1 \), \( l \) can only be 0, but here \( l = 1 \). Hence, this combination is not allowed.
- (C) is correct because \( n = 2, l = 1, m_l = +1, m_s = -\frac{1}{2} \) is allowed.
- (D) is correct because \( n = 3, l = 1, m_l = 0, m_s = +\frac{1}{2} \) is allowed.
Thus, the incorrect combination is option (B).