For the principal quantum number n = 2, the possible values of azimuthal quantum number and magnetic quantum number respectively are

Options

A. 0, 1 , 2 and 1, 2,3
B. 0, 1, 2 and -1, 0, +1
C. 0, 1 and -1, 0, +1
D. 1, 2, 3 and -1, 0, +1

Explanation

To solve the question regarding the possible values of the azimuthal quantum number (l) and the magnetic quantum number (m) for a principal quantum number (n) of 2, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Principal Quantum Number (n)**:
- The principal quantum number given is \( n = 2 \).

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 \( n = 2 \):
\[ l = 0, 1 \]
- The possible values of \( l \) are \( 0 \) and \( 1 \).

3. **Determine the Possible Values of the Magnetic Quantum Number (m)**:
- The magnetic quantum number \( m \) can take values ranging from \( -l \) to \( +l \).
- For \( l = 0 \):
\[ m = 0 \]
- For \( l = 1 \):
\[ m = -1, 0, +1 \]
- Thus, the possible values of \( m \) for \( l = 0 \) and \( l = 1 \) are:
- For \( l = 0 \): \( m = 0 \)
- For \( l = 1 \): \( m = -1, 0, +1 \)

4. **Summarize the Results**:
- The possible values of the azimuthal quantum number (l) are \( 0 \) and \( 1 \).
- The possible values of the magnetic quantum number (m) are \( -1, 0, +1 \) for \( l = 1 \) and \( 0 \) for \( l = 0 \).

5. **Final Answer**:
- Therefore, the possible values of the azimuthal quantum number and the magnetic quantum number respectively are:
- Azimuthal quantum number (l): \( 0, 1 \)
- Magnetic quantum number (m): \( -1, 0, +1 \)