For a particular value of azimuthal quantum number (I), the total number of magnetic quantum number values (m) is given by

Options

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

Answer

To determine the total number of magnetic quantum number values (m) for a particular value of the azimuthal quantum number (L), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Quantum Numbers**:
- The azimuthal quantum number (L) defines the shape of the orbital and can take on integer 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 on values ranging from -L to +L.

2. **Determine the Range of m**:
- For a given value of L, the possible values of the magnetic quantum number (m) are:
\[ m = -L, -L + 1, -L + 2, \ldots, 0, \ldots, L - 1, L \]
- This means that m can take on a total of \(2L + 1\) values.

3. **Formulate the Expression**:
- The total number of magnetic quantum number values (m) for a specific azimuthal quantum number (L) can be expressed mathematically as:
\[ \text{Total values of } m = 2L + 1 \]

4. **Conclusion**:
- Therefore, for a particular value of the azimuthal quantum number L, the total number of magnetic quantum number values m is given by the formula \(2L + 1\).

### Final Answer:
The total number of magnetic quantum number values (m) for a particular value of the azimuthal quantum number (L) is \(2L + 1\).

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