For a given value of 'l' the total number of 'm' values is `"____________"`

Answer

To solve the question "For a given value of 'l' the total number of 'm' values is ____________", we need to understand the relationship between the azimuthal quantum number (l) and the magnetic quantum number (m).

### Step-by-Step Solution:

1. **Understanding Quantum Numbers**:
- Quantum numbers are values that describe the unique quantum state of an electron in an atom. The main quantum numbers are:
- Principal quantum number (n)
- Azimuthal quantum number (l)
- Magnetic quantum number (m)
- Spin quantum number (s)

2. **Defining the Azimuthal Quantum Number (l)**:
- The azimuthal quantum number (l) determines the shape of the orbital and can take on integer values from 0 to (n-1), where n is the principal quantum number.

3. **Understanding the Magnetic Quantum Number (m)**:
- The magnetic quantum number (m) describes the orientation of the orbital in space. For a given value of l, the possible values of m range from -l to +l.

4. **Calculating the Total Number of m Values**:
- The total number of possible m values for a given l can be calculated using the formula:
\[ \text{Total m values} = 2l + 1 \]
- This formula accounts for all integer values from -l to +l, including zero.

5. **Examples**:
- If l = 0 (s orbital):
- m can be 0 → Total m values = 2(0) + 1 = 1
- If l = 1 (p orbital):
- m can be -1, 0, +1 → Total m values = 2(1) + 1 = 3
- If l = 2 (d orbital):
- m can be -2, -1, 0, +1, +2 → Total m values = 2(2) + 1 = 5
- If l = 3 (f orbital):
- m can be -3, -2, -1, 0, +1, +2, +3 → Total m values = 2(3) + 1 = 7

### Final Answer:
For a given value of 'l', the total number of 'm' values is **2l + 1**.