Given below are two statements:
Statement I: The energy of the He⁺ ion in n=2 state is same as the energy of H

Question

Given below are two statements:
Statement I: The energy of the He⁺ ion in n=2 state is same as the energy of H atom in n=1 state.
Statement II: It is possible to determine simultaneously the exact position and exact momentum of an electron in H atom.

In light of the above statements, choose the correct answer from the options given below:

Accepted Answer

1.  **Analyze Statement I:** According to Bohr's theory, the energy of an electron in the n-th orbit of a hydrogen-like species is given by $E_n \propto \frac{Z^2}{n^2}$.
    *   For Hydrogen atom (H): $Z=1$, $n=1$. Thus, $E_1(H) \propto \frac{1^2}{1^2} = 1$.
    *   For Helium ion ($He^+$): $Z=2$, $n=2$. Thus, $E_2(He^+) \propto \frac{2^2}{2^2} = 1$.
    *   Since the ratios are identical, the energies are the same ($E = -2.18 	imes 10^{-18} 	ext{ J}$). Therefore, Statement I is **True** .

2.  **Analyze Statement II:** According to Heisenberg's Uncertainty Principle, it is impossible to determine simultaneously the exact position and exact momentum (or velocity) of a microscopic particle like an electron . Therefore, Statement II is **False**.

Conclusion: Statement I is true and Statement II is false.

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