The magnatic quantum number for the valence electron of Caesium (atomic number 55) is

Options

A. 3
B. 0
C. `-3`
D. Any number between `+3` to -`3`.

Explanation

To determine the magnetic quantum number for the valence electron of Cesium (atomic number 55), we can follow these steps:

### Step 1: Identify the Electronic Configuration
Cesium (Cs) has an atomic number of 55. The electronic configuration of Cesium can be derived from the preceding noble gas, Xenon (Xe), which has an atomic number of 54. Thus, the electronic configuration of Cesium is:
\[ \text{Xe} \, 6s^1 \]

### Step 2: Determine the Principal Quantum Number (n)
In the electronic configuration \(6s^1\), the principal quantum number \(n\) is 6. This indicates that the valence electron is in the 6th energy level.

### Step 3: Determine the Azimuthal Quantum Number (l)
The azimuthal quantum number \(l\) is determined by the type of orbital. For an s orbital, \(l = 0\). Therefore, for the valence electron in the 6s orbital:
\[ l = 0 \]

### Step 4: Calculate the Magnetic Quantum Number (m)
The magnetic quantum number \(m\) can be calculated using the formula:
\[ m = -l, -l + 1, \ldots, +l \]
Since \(l = 0\), the only possible value for \(m\) is:
\[ m = 0 \]

### Conclusion
The magnetic quantum number for the valence electron of Cesium is:
\[ \text{m} = 0 \]

### Summary
- The electronic configuration of Cesium is \( \text{Xe} \, 6s^1 \).
- The principal quantum number \(n\) is 6.
- The azimuthal quantum number \(l\) is 0 (for s orbital).
- The magnetic quantum number \(m\) is 0.