**Worked Example: Find all possible quantum states of the hydrogen electron when the principal quantum number n = 2.** 1. **Principal quantum number (n):** n = 2. 2. **Angular momentum quantum number (l):** For n = 2, l can be 0 or 1. - If l = 0 (s‑orbital): - Magnetic quantum number m_l can only be 0. - Spin s can be +½ or –½. - States: (n=2,l=0,m_l=0,s=+½) and (n=2,l=0,m_l=0,s=–½). - If l = 1 (p‑orbital): - m_l can be –1, 0, or +1. - For each m_l, spin can be +½ or –½. - States: (n=2,l=1,m_l=–1,s=+½), (n=2,l=1,m_l=–1,s=–½), (n=2,l=1,m_l=0,s=+½), (n=2,l=1,m_l=0,s=–½), (n=2,l=1,m_l=+1,s=+½), (n=2,l=1,m_l=+1,s=–½). 3. **Count the total states:** 2 (from l=0) + 6 (from l=1) = 8 possible quantum states. **Answer:** When n = 2, the electron can occupy 8 distinct quantum states, each identified by a unique set of (n, l, m_l, s).