Step 1: Configuration
Potassium ($Z=19$): $1s^{2}, 2s^{2}, 2p^{6}, 3s^{2}, 3p^{6}, 4s^{1}$.
Step 2: Valence Electron
The outermost (valence) electron is in the $4s$ orbital ($4s^{1}$).
Step 3: Quantum Numbers
- Principal ($n$) = 4
- Azimuthal ($l$) for $s$-orbital = 0
- Magnetic ($m_{l}$) = 0
- Spin ($s$) = $+1/2$ or $-1/2$.
Step 4: Conclusion
The correct set is $4, 0, 0, 1/2$.
Final Answer: (c)