Q51 / 75 · JEE Main 2025 (2 Apr Shift 1) · Physics
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
Choose the correct answer from the options given below :
(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
Choose the correct answer from the options given below :
- A(B), (D) only
- Correct answerB(A), (B) only
- C(A), (D) only
- D(A), (C) only
Solution
$\begin{aligned} & \mathrm{E} \propto \frac{\mathrm{Z}}{\mathrm{n}^2} \\ & \mathrm{Z}_{\mathrm{H}}=1 \quad \mathrm{Z}_{\mathrm{He}^{+}}=2 \quad \mathrm{Z}_{\mathrm{Li}^{+2}}=3\end{aligned}$
$\begin{aligned} & 1^{\text {st }} \text { excited state } \Rightarrow \mathrm{n}=2 \\ & 2^{\text {nd }} \text { excited state } \Rightarrow \mathrm{n}=3\end{aligned}$
From the given statements only A \& B are correct.
$\begin{aligned} & 1^{\text {st }} \text { excited state } \Rightarrow \mathrm{n}=2 \\ & 2^{\text {nd }} \text { excited state } \Rightarrow \mathrm{n}=3\end{aligned}$
From the given statements only A \& B are correct.
Hence, the correct answer is option: 'B'.