AP EAMCET · PHYSICS · Atomic Physics

\(\mu\)-meson of charge ' \(e\) ', mass 208 me moves in a circular orbit around a heavy nucleus having charge \(+3 e\). The quantum state ' \(n\) ' for which the radius of the orbit is same as that of the first Bohr orbit for hydrogen atom ts [approximately]

A \(\mathrm{n} \approx 20\)
B \(\mathrm{n} \approx 25\)
C \(\mathrm{n} \approx 28\)
D \(\mathrm{n} \approx 29\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\mathrm{n} \approx 25\)

Step-by-step Solution

Detailed explanation

For hydrogen atom, \(r_n=\frac{n^2 h^2}{4 \pi^2 m k e^2} \Rightarrow r_1=\frac{h^2}{4 \pi^2 m k e^2}\) ....(i) For \(\mu\)-meson, \(\mathrm{m} \rightarrow 208 \mathrm{~m}, \mathrm{Z}=3\) \(\therefore r_n=\frac{n^2 h^2}{4 \pi^2(208 m) k(3) e^2}\) ....(ii) From eq(i) and (ii), we…

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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