Considering Bohr's atomic model: (A) the energy of H atom in ground state is the same as the energy of He⁺ ion in its first excited state; (B) the energy of H atom in ground state is the same as that of Li²⁺ ion in its second excited state; (C) the energy of H atom in ground state is the same as that of He⁺ ion in its ground state; (D) the energy of He⁺ ion in its first excited state is the same as that of Li²⁺ ion in its ground state. Choose the correct answer.
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Question

Considering Bohr's atomic model: (A) the energy of H atom in ground state is the same as the energy of He⁺ ion in its first excited state; (B) the energy of H atom in ground state is the same as that of Li²⁺ ion in its second excited state; (C) the energy of H atom in ground state is the same as that of He⁺ ion in its ground state; (D) the energy of He⁺ ion in its first excited state is the same as that of Li²⁺ ion in its ground state. Choose the correct answer.

Options

G1 Physics · Accepted Answer

For a hydrogen-like species, Eₙ = -13.6 Z²/n² eV. H ground state: Z=1, n=1 E = -13.6 eV. He⁺ first excited state: Z=2, n=2 E = -13.6×4/4 = -13.6 eV. So A is true. Li²⁺ second excited state: Z=3, n=3 E = -13.6×9/9 = -13.6 eV. So B is true. He⁺ ground state: Z=2, n=1 E = -54.4 eV, so C is false. Li²⁺ ground state: Z=3, n=1 E = -122.4 eV, which is not equal to the He⁺ first-excited-state energy. So D is false. Therefore only A and B are correct. Correct option: C.