The number of subshells associated with n = 4 and m = –2 quantum numbers is :

Options

A. 4
B. 8
C. 16
D. 2

Explanation

To determine the number of subshells associated with the quantum numbers \( n = 4 \) and \( m = -2 \), we need to follow these steps:

### Step-by-Step Solution:

1. **Determine the possible values of \( l \) for \( n = 4 \):**
- The principal quantum number \( n \) is given as 4.
- The azimuthal quantum number \( l \) can take values from 0 to \( n-1 \).
- Therefore, for \( n = 4 \), \( l \) can be 0, 1, 2, or 3.

2. **Identify the subshells corresponding to each \( l \) value:**
- \( l = 0 \) corresponds to the 4s subshell.
- \( l = 1 \) corresponds to the 4p subshell.
- \( l = 2 \) corresponds to the 4d subshell.
- \( l = 3 \) corresponds to the 4f subshell.

3. **Determine the possible values of \( m \) for each \( l \):**
- The magnetic quantum number \( m \) can take values from \( -l \) to \( +l \), including zero.
- For \( l = 0 \): \( m \) can be 0.
- For \( l = 1 \): \( m \) can be -1, 0, or 1.
- For \( l = 2 \): \( m \) can be -2, -1, 0, 1, or 2.
- For \( l = 3 \): \( m \) can be -3, -2, -1, 0, 1, 2, or 3.

4. **Identify which subshells have \( m = -2 \):**
- For \( l = 2 \) (4d subshell), \( m = -2 \) is one of the possible values.
- For \( l = 3 \) (4f subshell), \( m = -2 \) is one of the possible values.

5. **Count the number of subshells where \( m = -2 \):**
- From the above analysis, \( m = -2 \) is present in both the 4d and 4f subshells.

Therefore, the number of subshells associated with \( n = 4 \) and \( m = -2 \) is **2**.