Question

How many electrons in an atom may have the following quantum numbers?

1. n = 4, m_s = – \(\frac 12\)
2. n = 3, l = 0

Answer 1

(a) n = 4, m_s = −1/2

• For a given shell \(n\), maximum electrons = \(2n^2\).
• For \(n = 4\): maximum electrons = \(2 \times 4^2 = 2 \times 16 = 32\).
• Half of these have spin \(m_s = +\frac{1}{2}\) and half have \(m_s = -\frac{1}{2}\).
• So, electrons with \(n = 4\) and \(m_s = -\frac{1}{2}\) = \(32/2 = 16\).

Answer (a): 16 electrons

(b) n = 3, l = 0

• \(n = 3, l = 0\) corresponds to the 3s orbital.
• Any single s orbital can hold a maximum of 2 electrons (with opposite spins).

Answer (b): 2 electrons