What is the correct set of quantum numbers (n, l, m_l, m_s) for the only electron in the ground state of a He⁺ ion?
Answer
n=1, l=0, m_l=0, m_s=+½
The correct answer is n=1, l=0, m_l=0, m_s=+½ — Combine the values to obtain the set (1, 0, 0, +½).
Step-by-step solution
- Identify the principal quantum number for the ground state: n = 1.
- For a given n, the orbital quantum number l can take values from 0 to n-1, so l = 0.
- The magnetic quantum number m_l ranges from -l to +l; with l = 0, m_l must be 0.
- The spin quantum number m_s can be either +½ or –½; we choose +½ for the answer.
- Combine the values to obtain the set (1, 0, 0, +½).
Common mistake: Using l = 1 or assigning a non‑zero m_l for n = 1
Concept tested: Quantum numbers for hydrogen‑like ground state
Published · How this solution was prepared and checked
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