Considering Bohr's atomic model for hydrogen atom:
(A) the energy of H atom in ground state is same as energy of $\text{He}^+$ ion in its first excited state.
(B) the energy of H atom in ground state is same as that for $\text{Li}^{++}$ ion in its second excited state.
(C) the energy of H atom in its ground state is same as that of $\text{He}^+$ ion for its ground state.
(D) the energy of $\text{He}^+$ ion in its first excited state is same as that for $\text{Li}^{++}$ ion in its ground state.
Choose the correct answer from the options given below:
Answer: (B) (A), (B) only
For a hydrogen-like ion $E_n = -13.6\,\dfrac{Z^2}{n^2}\ \text{eV}$, so compare $Z^2/n^2$. H ground state: $1/1 = 1$.
- (A) $\text{He}^+$ ($Z = 2$), first excited state $n = 2$: $4/4 = 1$. Same. ✔
- (B) $\text{Li}^{++}$ ($Z = 3$), second excited state $n = 3$: $9/9 = 1$. Same. ✔
- (C) $\text{He}^+$ ground state: $4/1 = 4$. Different. ✘
- (D) $\text{He}^+$, $n = 2$: $1$; $\text{Li}^{++}$ ground state: $9$. Different. ✘
Only (A) and (B) are correct.
Solution by Sreeraj P, M.Sc Physics