MHT CET · Physics · Atomic Physics

An electron makes a transition from an excited state to the ground state of a ydrogen like atom. out of the following statements which one is correct?

A K.E., P.E. and T.E. decreases.
B K.E. decreases, P.E. increases but total energy remains the same.
C E. increases but P.E. and T.E. decreases.
D K.E. and T.E. decreases but P.E. increases.

Verified Solution

Answer & Solution

Correct Answer

(B) K.E. decreases, P.E. increases but total energy remains the same.

Step-by-step Solution

Detailed explanation

\(\begin{aligned}
\text { T.E. } &=-13.6 \frac{Z^{2}}{n^{2}} \mathrm{eV}, \text { P.E. }=2 \text { T.E. } \\
\text { and } k . E . &=13.6 \frac{Z^{2}}{n^{2}} \mathrm{eV}
\end{aligned}\)
Hence if n decreases k.E increases but P.E. and T.E. decrease.

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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