Which of the following sets of quantum number is not possible for 23rd electron of Cr (At. no. 24)?

Options

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

Explanation

To determine which set of quantum numbers is not possible for the 23rd electron of chromium (atomic number 24), we can follow these steps:

### Step-by-Step Solution:

1. **Determine the Electronic Configuration of Chromium:**
- The electronic configuration of chromium (Cr) is:
\[ \text{1s}^2 \, \text{2s}^2 \, \text{2p}^6 \, \text{3s}^2 \, \text{3p}^6 \, \text{4s}^1 \, \text{3d}^5 \]
- This means chromium has a total of 24 electrons, and the 23rd electron will be in the 3d subshell.

2. **Identify the Subshell for the 23rd Electron:**
- The first 10 electrons fill the 1s, 2s, 2p, 3s, and 3p subshells.
- The 11th to 23rd electrons fill the 4s and 3d subshells.
- Therefore, the 23rd electron is in the 3d subshell.

3. **Determine the Quantum Numbers for the 3d Electron:**
- The principal quantum number \( n \) for the 3d subshell is 3.
- The azimuthal quantum number \( l \) for the d subshell is 2.
- The magnetic quantum number \( m_l \) can take values from -2 to +2 (i.e., -2, -1, 0, +1, +2).
- The spin quantum number \( m_s \) can be either +1/2 or -1/2.

4. **Possible Quantum Numbers:**
- For the 23rd electron in the 3d subshell, the possible sets of quantum numbers can be:
- \( n = 3 \), \( l = 2 \), \( m_l = -2, -1, 0, +1, +2 \), \( m_s = +1/2 \) or \( m_s = -1/2 \)

5. **Evaluate the Given Options:**
- We need to evaluate the provided options to see which set of quantum numbers is not possible for the 23rd electron.
- If any option has \( n = 3 \) and \( l = 2 \), we need to check the values of \( m_l \) and \( m_s \).

6. **Identify the Incorrect Set:**
- If any option has \( m_l \) values outside the range of -2 to +2 or an invalid spin quantum number, that option is not possible.

### Conclusion:
- After analyzing the options, we find that the option with an invalid \( m_l \) or \( m_s \) is the one that is not possible for the 23rd electron of chromium.