No. of subshells having n=4 & m = (-2) are

Options

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

Answer

To solve the question regarding the number of subshells having n = 4 and m = -2, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Principal Quantum Number (n)**:
- The principal quantum number (n) is given as 4. This indicates that we are looking at the fourth energy level.

2. **Determine the Possible Values of the Azimuthal Quantum Number (l)**:
- The azimuthal quantum number (l) can take values from 0 to (n - 1). Therefore, for n = 4:
- Possible values of l: 0, 1, 2, 3
- This corresponds to subshells:
- l = 0 → s subshell (4s)
- l = 1 → p subshell (4p)
- l = 2 → d subshell (4d)
- l = 3 → f subshell (4f)

3. **Determine the Possible Values of the Magnetic Quantum Number (m)**:
- The magnetic quantum number (m) can take values from -l to +l. We need to find cases where m = -2.
- For each value of l:
- If l = 0: m can only be 0 (not applicable)
- If l = 1: m can be -1, 0, +1 (not applicable)
- If l = 2: m can be -2, -1, 0, +1, +2 (applicable)
- If l = 3: m can be -3, -2, -1, 0, +1, +2, +3 (applicable)

4. **Count the Valid Subshells**:
- From the above analysis, we find that m = -2 is valid for:
- l = 2 (4d subshell)
- l = 3 (4f subshell)
- Therefore, the valid subshells for n = 4 and m = -2 are:
- 4d (l = 2, m = -2)
- 4f (l = 3, m = -2)

5. **Final Count**:
- The total number of subshells that satisfy the conditions n = 4 and m = -2 is 2.

### Answer:
The number of subshells having n = 4 and m = -2 is **2**.