CUET · PHYSICS · PYQ PAPER 2023

If \(E _{ p }\) and \(E _{ k }\) represents the potential and kinetic energy respectively of an orbital electron, then according to Bohr's theory.

A \(E_k=-\frac{E_p}{2}\)
B \(E _{ L }=- E _{ p }\)
C \(E _{ k }=-2 E _{ p }\)
D \(E _{ k }=2 E _{ p }\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(E_k=-\frac{E_p}{2}\)

Step-by-step Solution

Detailed explanation

In Bohr's model, kinetic energy is expressed as \(\frac{k Z e^2}{2 r}\) while potential energy is \(-\frac{k Z e^2}{r}\). Since \(E_p\) is exactly double the magnitude of \(E_k\) and opposite in sign, the correct mathematical relationship is \(E_k=-\frac{E_p}{2}\).

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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List-I	List-II
(A) Resonant frequency	(I) \( \frac{\omega L}{R} \)
(B) Quality factor	(II) \( 2\pi f L \)
(C) \( X_L \)	(III) \( \frac{1}{2\pi\sqrt{LC}} \)
(D) \( X_C \)	(IV) \( 1/2\pi f c \)