COMEDK · Physics · 28. Atomic Physics

In a hydrogen atom, if electron is replaced by a particle which is 40 times heavier but has the same charge, then, the ratio of the radius of the first excited state of a normal hydrogen atom to the ground state of the above atom is

A 40 : 1
B 1 : 160
C 1 : 40
D 160 : 1

Verified Solution

Answer & Solution

Correct Answer

(D) 160 : 1

Step-by-step Solution

Detailed explanation

The radius of the \(n\)-th orbit of a hydrogen-like atom is given by \(r_n = \dfrac{n^2 a_0}{Z} \times \dfrac{m_e}{m}\), where \(m\) is the mass of the particle and \(a_0\) is the Bohr radius of the hydrogen atom (\(a_0 = \dfrac{h^2}{4\pi^2 m_e e^2}\)). For a normal hydrogen…

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.

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