Atoms & Nuclei

JEE Main level, single correct, medium

9 of 239

Question 9 of 239

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

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Answer: (B) (A), (B) only

E∝Zn2ZH=1ZHe+=2ZLi+2=3\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}
1st  excited state ⇒n=22nd  excited state ⇒n=3\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.

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