Question

Considering Bohr’s atomic model for hydrogen atom :
(A) the energy of H atom in ground state is same as energy of He+ ion in its first excited state. 
(B) the energy of H atom in ground state is same as that for Li++ ion in its second excited state. 
(C) the energy of H atom in its ground state is same as that of He+ ion for its ground state. 
(D) the energy of He+ ion in its first excited state is same as that for Li++ ion in its ground state.

• A. (B), (C) only
• B. (A), (B) only
• C. (A), (D) only
• D. (A), (C) only

Hint:

In Bohr's atomic model, the energy levels depend on the atomic number \( Z \) and the principal quantum number \( n \). For ions like He\(^+\) and Li\(^2+\), the energy will differ due to their increased nuclear charge.

Answer 1

The Correct Option is B

The energy of an electron in a specific orbit is determined by the formula: \[ E \propto \frac{Z}{n^2} \]. For a hydrogen atom, \( Z_H = 1 \); for He\(^+\), \( Z_{He^+} = 2 \); and for Li\(^2+\), \( Z_{Li^{2+}} = 3 \). The first excited state corresponds to \( n = 2 \), and the second excited state corresponds to \( n = 3 \). Based on these statements, only options (A) and (B) are accurate.