JEE Mains · Physics · STD 12 - 11. Dual nature of radiation and matter

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason \(\mathrm{R}\)
Assertion A: In photoelectric effect, on increasing the intensity of incident light the stopping potential increases.
Reason R : Increase in intensity of light increases the rate of photoelectrons emitted, provided the frequency of incident light is greater than threshold frequency.
In the light of the above statements, choose the correct answer from the options given below

A Both \(\mathrm{A}\) and \(\mathrm{R}\) are true but \(\mathrm{R}\) is NOT the correct explanation of \(\mathrm{A}\)
B \(\mathrm{A}\) is false but \(\mathrm{R}\) is true
C \(\mathrm{A}\) is true but \(\mathrm{R}\) is false
D Both \(\mathrm{A}\) and \(\mathrm{R}\) are true and \(\mathrm{R}\) is the correct explanation of \(\mathrm{A}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\mathrm{A}\) is false but \(\mathrm{R}\) is true

Step-by-step Solution

Detailed explanation

\(\mathrm{V}_{\mathrm{S}}=\frac{\mathrm{hv}-\phi}{\mathrm{e}}\) so stopping potential doesn't depend on Intensity \(\mathrm{I}=\frac{\eta \mathrm{hv}}{\mathrm{~A}}\) On increasing intensity no. of photons per sec. \(n\) increases so the no. of electrons.

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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