The four quantum numbers for the electron in the outermost orbital of potassium (atomic number 19) are:

🧠 The 19th Electron's Address To find the quantum numbers of the outermost electron, we first need to know which house it lives in. Potassium ($Z=19$) follows the Aufbau principle, filling orbits by the $(n+l)$ rule.

🗺️ The Electronic Mapping

1. Configuration: $1s^2 2s^2 2p^6 3s^2 3p^6 4s^1$. The last electron enters the 4s orbital.
2. Quantum Numbers:
   • $n$ (Principal) = 4 (indicated by the coefficient)
   • $l$ (Azimuthal) = 0 (for s-subshell)
   • $m_l$ (Magnetic) = 0 (only possible value for $l=0$)
   • $s$ (Spin) = $+1/2$ (standard for the single electron).

⚡ The Argon Core Shortcut Instead of writing the whole list, remember Potassium is the start of Period 4. Its outer electron must be in the first subshell of the 4th shell, which is $4s^1$. This gives $n=4$ and $l=0$ instantly.

⚠️ Common Traps Many students expect the 19th electron to go into the $3d$ orbital because $n=3$ is "next" after $3p$. But according to the $(n+l)$ rule, $4s$ ($4+0=4$) is lower energy than $3d$ ($3+2=5$). Potassium is the classic test of this rule!

$\boxed{\text{Answer: (b)}}$