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For the hydrogen‑like ion He⁺ (nuclear charge Z=2), which set of quantum numbers (n, l, m_l, m_s) correctly describes its only electron in the ground state?

easy MCQ 1 mark Class 12 · Physics · Atoms
  1. (1, 0, 0, +½)
  2. (1, 1, 0, –½)
  3. (2, 0, 0, +½)
  4. (1, 0, 1, +½)
Answer
(1, 0, 0, +½)

The correct answer is (1, 0, 0, +½) — Thus the correct set is (1, 0, 0, +½).

Step-by-step solution

  1. The ground state corresponds to the lowest principal quantum number n=1.
  2. For n=1 the orbital quantum number must be l=0 (since l ranges from 0 to n‑1).
  3. With l=0 the magnetic quantum number m_l can only be 0.
  4. The spin quantum number m_s can be +½ or –½; any one is allowed for a single electron.
  5. Thus the correct set is (1, 0, 0, +½).
Common mistake: Choosing l=1 or assigning m_l≠0 for n=1

Concept tested: Quantum numbers for hydrogen‑like ion

Published · How this solution was prepared and checked

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