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 find the relationship between the magnetic quantum number (m) and the azimuthal quantum number (l), we can 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 values from 0 to n-1, where n is the principal quantum number.
- The magnetic quantum number (m) describes the orientation of the orbital in space and can take values from -l to +l.

2. **Range of Magnetic Quantum Number**:
- The magnetic quantum number (m) can have values that range from -l to +l. This means:
\[ m = -l, -l + 1, ..., 0, ..., l - 1, l \]
- The total number of possible values for m is given by:
\[ \text{Total values of } m = 2l + 1 \]

3. **Finding the Relation**:
- From the above, we can express the relationship between m and l. Since m can take values from -l to +l, we can rearrange the equation:
\[ m = -l, -l + 1, ..., l \]
- Therefore, the total number of values for m, which is \(2l + 1\), indicates that:
\[ m \text{ can take values from } -l \text{ to } +l \]

4. **Expressing l in terms of m**:
- If we want to express l in terms of m, we can rearrange the equation:
\[ l = \frac{m + 1}{2} \]
- This shows how l can be derived from m.

5. **Final Relation**:
- Thus, the final relation between the magnetic quantum number (m) and the azimuthal quantum number (l) can be summarized as:
\[ l = \frac{m - 1}{2} \]