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 solve the question about the number of subshells associated with the quantum numbers \( n = 4 \) and \( m = -2 \), we can follow these steps:

### Step 1: Understand the Quantum Numbers
The principal quantum number \( n \) indicates the energy level of the electron in an atom. The azimuthal quantum number \( l \) determines the shape of the subshell and can take values from \( 0 \) to \( n-1 \). The magnetic quantum number \( m \) can take values from \( -l \) to \( +l \).

### Step 2: Determine Possible Values of \( l \)
Given \( n = 4 \):
- The possible values of \( l \) are \( 0, 1, 2, 3 \).

### Step 3: Determine Possible Values of \( m \) for Each \( l \)
Now, we will find the possible values of \( m \) for each \( l \):
- For \( l = 0 \): \( m \) can only be \( 0 \) (not applicable since \( m = -2 \)).
- For \( l = 1 \): \( m \) can be \( -1, 0, +1 \) (not applicable since \( m = -2 \)).
- For \( l = 2 \): \( m \) can be \( -2, -1, 0, +1, +2 \) (applicable since \( m = -2 \)).
- For \( l = 3 \): \( m \) can be \( -3, -2, -1, 0, +1, +2, +3 \) (applicable since \( m = -2 \)).

### Step 4: Count the Valid Subshells
From the above analysis:
- The valid \( l \) values that correspond to \( m = -2 \) are \( l = 2 \) and \( l = 3 \).

### Step 5: Conclusion
Thus, the number of subshells associated with \( n = 4 \) and \( m = -2 \) is **2**.

### Final Answer
The answer is option D: **2**.

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