Question

a single electron in an orbital has quantum numbers ( n = 2, l = 0, m_l = 0, m_s = +\frac{1}{2} ). what are the quantum numbers for the next electron added to this atom? answer: a ( n = 2, l = 1, m_l = 0, m_s = +\frac{1}{2} ) b ( n = 2, l = 0, m_l = 0, m_s = -\frac{1}{2} ) c ( n = 2, l = 0, m_l = 0, m_s = +\frac{1}{2} ) d ( n = 2, l = 1, m_l = 0, m_s = -\frac{1}{2} ) e ( n = 2, l = 1, m_l = 1, m_s = -\frac{1}{2} )

Explanation:

Step1: Apply Pauli Exclusion Principle

According to Pauli Exclusion Principle, no two electrons in an atom can have the same set of four quantum numbers.

Step2: Determine quantum numbers

For the given electron \(n = 2\), \(l=0\), \(m_l = 0\), \(m_s=+\frac{1}{2}\). The next electron added to the same orbital (since orbitals fill with opposite - spin electrons first) will have \(n = 2\), \(l = 0\), \(m_l=0\) (same orbital) and \(m_s=-\frac{1}{2}\) (opposite spin).

Answer:

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