The energy of He⁺ ion in its first excited state is, (The ground state energy for the Hydrogen atom is -13.6 eV) :

Solution

Physics sir · 4 steps

Use Eₙ = -13.6 Z²/n² with Z = 2 and n = 2: the Z² and the n² cancel each other.

1. Hydrogen-like formula. He⁺ has a single electron, so the Bohr formula for hydrogen works with the nuclear charge Z included.

   Eₙ = -13.6 Z²/n² eV

2. Pick Z and n. Helium has Z = 2. The ground state is n = 1, so the first excited state is n = 2.
3. Put in numbers. E₂ = -13.6 × 2²/2² = -13.6 × 4/4 = -13.6 eV.
4. So. The energy of He⁺ in its first excited state is -13.6 eV, option (a).

The idea to keep. For any one-electron ion, energy goes as Z²/n². The first excited state means n = 2, not n = 1. Fix both numbers before you put anything into the formula.

Answer from the NTA final answer key. Solution by PrepWiser.