When the value of n = 2, m can have

Options

A. 1 value
B. 3 values
C. 4 values
D. 7 values.

Answer

To determine the possible values of the magnetic quantum number (m) when the principal quantum number (n) is equal to 2, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Principal Quantum Number (n)**:
- Given that \( n = 2 \).

2. **Determine the Azimuthal Quantum Number (l)**:
- The azimuthal quantum number \( l \) can take values from \( 0 \) to \( n-1 \).
- Therefore, when \( n = 2 \), \( l \) can be:
- \( l = 0 \) (s orbital)
- \( l = 1 \) (p orbital)

3. **Determine the Magnetic Quantum Number (m)**:
- The magnetic quantum number \( m \) can take values from \( -l \) to \( +l \).
- For \( l = 0 \):
- \( m \) can only be \( 0 \) (1 value).
- For \( l = 1 \):
- \( m \) can take values \( -1, 0, +1 \) (3 values).

4. **Count the Total Possible Values of m**:
- From \( l = 0 \): 1 value (m = 0).
- From \( l = 1 \): 3 values (m = -1, 0, +1).
- Total possible values of \( m \) when \( n = 2 \) is \( 1 + 3 = 4 \).

### Final Answer:
When \( n = 2 \), the magnetic quantum number \( m \) can have **4 values**.

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