To determine the correct set of quantum numbers for the valence electron of rubidium (Z = 37), we first need to find its electronic configuration. The atomic number Z = 37 means rubidium has 37 electrons.

Step 1: Electronic Configuration
The order of filling orbitals is: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p.
For Rb (37):
$1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^{10}4p^{6}5s^1$
Total electrons: 2+2+6+2+6+2+10+6+1 = 37. The valence electron is in the 5s orbital.

Step 2: Quantum Numbers for 5s¹ Electron
Quantum numbers describe an electron's state and are defined as:
- Principal quantum number (n): energy level, for 5s, n = 5.
- Azimuthal quantum number (l): shape of orbital. For s orbital, l = 0.
- Magnetic quantum number (m_l): orientation. For l=0, m_l can only be 0.
- Spin quantum number (m_s): electron spin, which can be +1/2 or -1/2.

For the single valence electron in 5s¹:
n = 5, l = 0, m_l = 0, m_s = +1/2 (or -1/2, but typically +1/2 is chosen for the first electron).

Step 3: Compare with Options
The correct set is: 5, 0, 0, +1/2.

Final Answer: The correct quantum numbers are $5,0,0,+\frac{1}{2}$

Related Topics and Formulae

Quantum Numbers:
- n (Principal): Positive integer (1,2,3,...), indicates shell.
- l (Azimuthal): Integer from 0 to n-1. l=0 (s), l=1 (p), l=2 (d), l=3 (f).
- m_l (Magnetic): Integer from -l to +l.
- m_s (Spin): +1/2 or -1/2.

Electronic Configuration Rules:
- Aufbau Principle: Electrons fill lowest energy orbitals first.
- Pauli Exclusion Principle: No two electrons can have same set of four quantum numbers.
- Hund's Rule: Orbitals are filled singly before pairing.