The four quantum numbers of the valence electron of potassium atom are :

Question

Accepted Answer

The question asks for the four quantum numbers of the valence electron of a potassium atom. Let's analyze why Option 3 is the correct answer and why the other options are incorrect.

### Explanation for Option 3: 4, 0, 0, 1/2

1. **Principal Quantum Number (n):** 
   - Potassium has an atomic number of 19, and its electron configuration is $1s^2 2s^2 2p^6 3s^2 3p^6 4s^1$.
   - The valence electron is in the 4s orbital, so the principal quantum number $n$ is 4.

2. **Azimuthal Quantum Number (l):**
   - The azimuthal quantum number $l$ defines the shape of the orbital. For an s orbital, $l = 0$.
   - Since the valence electron is in the 4s orbital, $l$ is 0.

3. **Magnetic Quantum Number (m\_l):**
   - The magnetic quantum number $m\_l$ describes the orientation of the orbital. For $l = 0$, $m\_l$ can only be 0.

4. **Spin Quantum Number (m\_s):**
   - The spin quantum number $m\_s$ can be either $+1/2$ or $-1/2$. The given option uses $+1/2$, which is a valid choice for the spin of an electron.

Thus, the quantum numbers 4, 0, 0, 1/2 correctly describe the valence electron of a potassium atom, making Option 3 the correct answer.

### Explanation for Why Other Options are Incorrect:

1. **Option 1: 4, 0, -1, 1/2**
   - The azimuthal quantum number $l$ is correctly 0 for an s orbital, but the magnetic quantum number $m\_l$ is incorrectly given as -1. For $l = 0$, $m\_l$ must be 0.

2. **Option 2: 4, 1, 0, 1/2**
   - The azimuthal quantum number $l$ is incorrectly given as 1, which corresponds to a p orbital. The valence electron of potassium is in an s orbital, so $l$ should be 0.

3. **Option 4: 4, 1, 1, -1/2**
   - Similar to Option 2, the azimuthal quantum number $l$ is incorrectly given as 1. Additionally, the magnetic quantum number $m\_l$ is incorrectly given as 1, which is not possible for an s orbital where $l = 0$.

In conclusion, Option 3 is the only set of quantum numbers that accurately describes the valence electron of a potassium atom, adhering to the rules of quantum mechanics.