Considering Bohr;'s atomic model for hydrogen aton: (A) the energy of H atom in ground state is same as energy of ion in its first excited state. (B) the energy of H atom in ground state is same as that for ion in its second excitred state. (C) the e

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Solution

Q.
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.

Choose the correct answer from the options given below: [2025]

1 (B), (D) only

2 (A), (B) only

3 (A), (D) only

4 (A), (C) only

Ans.
(2)

$E = - 13.6 \frac{z_{2}}{n^{2}} eV$

$E_{{He}^{+}} 1^{st}$ excited state = –13.6 eV

$E_{{Li}^{2 +}} 2^{nd}$ excited state = –13.6 eV

(A), (B) are correct.

$E \propto \frac{Z}{n^{2}}$

$Z_{H} = 1 Z_{{He}^{+}} = 2 Z_{{Li}^{+ 2}} = 3$

$1^{st}$ excited state $\Rightarrow$ n = 2

$2^{nd}$ excited state $\Rightarrow$ n = 3

From the given statements only (A) and (B) are correct.

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