The correct set of quantum numbers for 4d-electrons is

Options

A. `4,3,2,+1//2`
B. 4,2,1,0
C. `4,3,-2,+1//2`
D. `4,2,1,-1//2`

Explanation

To determine the correct set of quantum numbers for 4d-electrons, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Principal Quantum Number (n)**:
- For 4d electrons, the principal quantum number \( n \) is 4.

2. **Determine the Azimuthal Quantum Number (l)**:
- The d subshell corresponds to an azimuthal quantum number \( l \) of 2.
- Therefore, \( l = 2 \).

3. **Find the Magnetic Quantum Number (m_l)**:
- The magnetic quantum number \( m_l \) can take values from \(-l\) to \(+l\).
- For \( l = 2 \), \( m_l \) can be \(-2, -1, 0, +1, +2\).
- Thus, \( m_l \) can be any of these values.

4. **Determine the Spin Quantum Number (m_s)**:
- The spin quantum number \( m_s \) can be either \( +\frac{1}{2} \) or \( -\frac{1}{2} \).
- Therefore, \( m_s \) can be \( +\frac{1}{2} \) or \( -\frac{1}{2} \).

5. **Compile the Possible Sets of Quantum Numbers**:
- A complete set of quantum numbers for a 4d electron can be represented as:
- \( n = 4 \)
- \( l = 2 \)
- \( m_l = -2, -1, 0, +1, +2 \)
- \( m_s = +\frac{1}{2} \) or \( -\frac{1}{2} \)

6. **Select the Correct Option**:
- From the options provided, we need to ensure that \( l = 2 \), \( m_l \) is one of the valid values, and \( m_s \) is either \( +\frac{1}{2} \) or \( -\frac{1}{2} \).
- The correct choice must reflect these values. The option that includes \( l = 2 \) and a valid \( m_l \) and \( m_s \) will be the correct answer.

### Final Answer:
The correct set of quantum numbers for 4d-electrons is \( n = 4 \), \( l = 2 \), \( m_l = -2, -1, 0, +1, +2 \), and \( m_s = +\frac{1}{2} \) or \( -\frac{1}{2} \). The correct option is option D.

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