If the radius of electron in the excited state of \(\mathrm{He}^{+}\)is \(0.4232 \mathrm{~nm}\), the energy of electron in that excited state in \(\mathrm{J}\) is :
(The radius and energy of electron in the first orbit of hydrogen atom are \(52.9 \mathrm{pm}\) and \(-2.18 \times 10^{-18} \mathrm{~J}\) respectively)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.