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The energy of a hydrogen atom in the ground state is −13.6 eV. The energy of He⁺ ion in the first excited state will be

1. −13.6 eV
2. −27.2 eV
3. −54.4 eV
4. −6.8 eV

Correct answer: −6.8 eV

Solution

The energy of an electron in a hydrogen-like atom is given by the formula E = -13.6 Z²/n² eV, where Z is the atomic number and n is the principal quantum number. For He⁺ (Z=2) in the first excited state (n=2), E = -13.6 × 2² / 2² = -6.8 eV.

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