Question

a single electron in an orbital has quantum numbers ( n = 2,ell = 0,m_{l}=0,) ( m_{s}=+\frac{1}{2}). what are the quantum numbers for the next electron added to this atom?

Explanation:

Step1: Apply Pauli Exclusion Principle

The Pauli Exclusion Principle states that no two electrons in an atom can have the same set of four quantum numbers. The given electron has \(n = 2\), \(l=0\), \(m_l = 0\), \(m_s=+\frac{1}{2}\). For the next electron in the same \(n = 2\) shell, if \(l = 0\) (s - orbital), the only other possibility for \(m_s\) is \(-\frac{1}{2}\) while keeping \(n = 2\), \(l = 0\), \(m_l=0\) (since for \(l = 0\), \(m_l\) can only be \(0\)).

Answer:

B. \(n = 2\), \(l = 0\), \(m_l=0\), \(m_s =-\frac{1}{2}\)