If m = magnetic quantum number and l = azimuthal quantum number then :-

Options

A. `m=l+2`
B. `m=2l^(2)+1`
C. `l=(m-1)/(2)`
D. `l=2m+1`

Answer

To solve the question regarding the relationship between the magnetic quantum number (m) and the azimuthal quantum number (l), we will follow these steps:

### Step-by-Step Solution:

1. **Understanding Quantum Numbers**:
- The azimuthal quantum number (l) determines the shape of the orbital and can take on integer values starting from 0. The possible values of l are:
- l = 0 (s orbital)
- l = 1 (p orbital)
- l = 2 (d orbital)
- l = 3 (f orbital)

2. **Determining the Magnetic Quantum Number (m)**:
- The magnetic quantum number (m) describes the orientation of the orbital in space. The values of m depend on l and range from -l to +l, including zero. Thus, for a given l:
- For l = 0, m = 0 (1 value)
- For l = 1, m = -1, 0, +1 (3 values)
- For l = 2, m = -2, -1, 0, +1, +2 (5 values)
- For l = 3, m = -3, -2, -1, 0, +1, +2, +3 (7 values)

3. **Finding the Relationship**:
- The relationship between m and l can be expressed mathematically as:
\[ m = 2l + 1 \]
- This means that for any given value of l, the corresponding value of m can be calculated.

4. **Rearranging the Equation**:
- To find l in terms of m, we can rearrange the equation:
\[ l = \frac{m - 1}{2} \]

5. **Conclusion**:
- From the relationship \( m = 2l + 1 \), we can conclude that if we know the value of m, we can find l using the rearranged formula \( l = \frac{m - 1}{2} \).

### Final Answer:
The relationship between the magnetic quantum number (m) and the azimuthal quantum number (l) is given by:
\[ m = 2l + 1 \]
And rearranging gives:
\[ l = \frac{m - 1}{2} \]