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

[JEE Main 2025, 2 Apr (Shift 1)]

Question

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

[JEE Main 2025, 2 Apr (Shift 1)]

YESPYQ · Accepted Answer

Correct answer: b) (A), (B) only. According to Bohr’s atomic model, the energy of an electron in a hydrogen-like atom is: $E=−13.6\frac{{Z}^{2}}{{n}^{2}}\mathrm{eV}$ Energy of H atom in ground state: $E=−13.6\mathrm{eV}$ Energy of He⁺ ion in first excited state: $E=−13.6\frac{{2}^{2}}{{2}^{2}}\mathrm{eV}$$=−13.6\mathrm{eV}$ Energy of Li²⁺ ion in second excited state: $E=−13.6\frac{{3}^{2}}{{3}^{2}}\mathrm{eV}$$=−13.6\mathrm{eV}$ Final Answer: $\mathrm{Correct}\mathrm{options}=A,B$

Considering Bohr's atomic model for hydrogen atom : (A) the energy of H atom in ground state is same as energy of \({\ma…

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