The maximum number of electrons that can be present in an orbit with s = +1/2 and l=2

Options

A. 1
B. 3
C. 5
D. 7

Answer

To determine the maximum number of electrons that can be present in an orbit with a spin quantum number (s) of +1/2 and an azimuthal quantum number (l) of 2, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Azimuthal Quantum Number (l)**:
- The azimuthal quantum number (l) indicates the shape of the orbital. For l = 2, this corresponds to the d subshell.

2. **Determine the Magnetic Quantum Number (m_l)**:
- The magnetic quantum number (m_l) can take values from -l to +l, including zero. Therefore, for l = 2:
\[ m_l = -2, -1, 0, +1, +2 \]
- This gives us a total of 5 possible values for m_l.

3. **Calculate the Maximum Number of Electrons**:
- Each orbital can hold a maximum of 2 electrons (one with spin +1/2 and one with spin -1/2).
- Since there are 5 orbitals (as determined from the m_l values), the maximum number of electrons in the d subshell is:
\[ \text{Maximum Electrons} = \text{Number of Orbitals} \times 2 = 5 \times 2 = 10 \]

4. **Consider the Spin Quantum Number (s)**:
- The question specifies that the spin quantum number (s) is +1/2. This indicates that we are considering only the electrons with this specific spin orientation.
- Therefore, if we are only counting the electrons with s = +1/2, we can place one electron in each of the 5 orbitals.

5. **Final Answer**:
- Thus, the maximum number of electrons that can be present in an orbit with s = +1/2 and l = 2 is 5.

### Conclusion:
The maximum number of electrons that can be present in an orbit with s = +1/2 and l = 2 is **5 electrons**.

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