The correct set of four quantum numbers for outermost electron of potassium (Z = 19) is:

Options

A. `4,1,0,(1)/(2)`
B. `3,1,0,(1)/(2)`
C. `4,0,0,(1)/(2)`
D. `3,0,0,(1)/(2)`

Explanation

To determine the correct set of four quantum numbers for the outermost electron of potassium (K), which has an atomic number (Z) of 19, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the Electronic Configuration**:
- The atomic number of potassium (K) is 19. The electronic configuration can be written as:
\[ \text{K: } 1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 4s^1 \]
- This shows that the outermost electron is in the 4s subshell.

2. **Identify the Principal Quantum Number (n)**:
- The principal quantum number (n) corresponds to the energy level of the electron. For the outermost electron in the 4s subshell, we have:
\[ n = 4 \]

3. **Determine the Azimuthal Quantum Number (l)**:
- The azimuthal quantum number (l) defines the subshell. For an s subshell, \( l = 0 \):
\[ l = 0 \quad (\text{for } s \text{ subshell}) \]

4. **Identify the Magnetic Quantum Number (m_l)**:
- The magnetic quantum number (m_l) describes the orientation of the orbital. For an s subshell, there is only one orientation:
\[ m_l = 0 \]

5. **Determine the Spin Quantum Number (s)**:
- The spin quantum number (s) indicates the spin of the electron. Since there is one unpaired electron in the 4s subshell, the spin can be either +1/2 or -1/2. We typically denote it as:
\[ s = +\frac{1}{2} \quad (\text{for the unpaired electron}) \]

6. **Compile the Quantum Numbers**:
- Now, we can compile the four quantum numbers for the outermost electron of potassium:
\[ \text{Quantum Numbers: } (n, l, m_l, s) = (4, 0, 0, +\frac{1}{2}) \]

### Final Answer:
The correct set of four quantum numbers for the outermost electron of potassium (K) is:
\[ (4, 0, 0, +\frac{1}{2}) \]