To determine the correct set of quantum numbers for the valence electron of rubidium (Rb), we need to understand the electronic configuration and the meaning of quantum numbers.
Electronic Configuration: Rubidium has an atomic number \( Z = 37 \). Its electronic configuration is:
\[
1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^1
\]
The valence electron is the outermost electron, which is in the \( 5s \) orbital.
Quantum Numbers Explanation:
Principal Quantum Number \((n)\): This indicates the main energy level. For Rubidium's valence electron in the \( 5s \) orbital, \( n = 5 \).
Azimuthal Quantum Number \((l)\): This defines the shape of the orbital. For an \( s \)-orbital, \( l = 0 \).
Magnetic Quantum Number \((m_l)\): This represents the orientation of the orbital in space. For \( l = 0 \), \( m_l = 0 \) because there is only one orientation possible for an \( s \)-orbital.
Spin Quantum Number \((m_s)\): It can be \( +\frac{1}{2} \) or \( -\frac{1}{2} \). For simplicity, we usually consider \( m_s = +\frac{1}{2} \) for singly occupied orbitals unless specified otherwise.
Combining these, the correct set of quantum numbers for the valence electron in Rubidium is:
\[
n = 5, \, l = 0, \, m_l = 0, \, m_s = +\frac{1}{2}
\]
Thus, the correct answer is \(5,0,0,+\frac{1}{2}\).
