Consider Xenon `(Z=54)`. The maximum number of electrons in this atom that have the values for their quantum numbers as `n=4, l=3` and `s=1/2` in its ground state is:

Options

A. Zero
B. `7`
C. `9`
D. `14`

Answer

To determine the maximum number of electrons in a Xenon atom that can have the quantum numbers \( n = 4 \), \( l = 3 \), and \( s = \frac{1}{2} \) in its ground state, we follow these steps:

### Step 1: Understand the Quantum Numbers
- The principal quantum number \( n \) indicates the energy level of the electron. Here, \( n = 4 \) means we are looking at the fourth energy level.
- The azimuthal quantum number \( l \) defines the subshell. For \( l = 3 \), this corresponds to the f subshell (since \( l = 0 \) is s, \( l = 1 \) is p, \( l = 2 \) is d, and \( l = 3 \) is f).
- The spin quantum number \( s \) can take values of \( +\frac{1}{2} \) or \( -\frac{1}{2} \).

### Step 2: Determine the Electron Configuration of Xenon
- Xenon (Xe) has an atomic number of 54, which means it has 54 electrons.
- The electron configuration of Xenon is:
\[ 1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 4s^2, 3d^{10}, 4p^6 \]
- This configuration shows that all the orbitals up to \( 4p \) are filled, and the \( 4f \) subshell is not occupied in the ground state of Xenon.

### Step 3: Analyze the \( 4f \) Subshell
- The \( 4f \) subshell can hold a maximum of 14 electrons (since each f subshell can hold \( 2(2l + 1) = 2(2 \cdot 3 + 1) = 14 \)).
- However, in the ground state of Xenon, the \( 4f \) subshell is not filled because it comes after the \( 4p \) subshell in the order of filling.

### Step 4: Conclusion
- Since the \( 4f \) subshell is not occupied in the ground state of Xenon, there are **0 electrons** that can have the quantum numbers \( n = 4 \), \( l = 3 \), and \( s = \frac{1}{2} \).

### Final Answer
The maximum number of electrons in Xenon with the specified quantum numbers is **0**.

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