Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\) : The photoelectric effect does not take place, if the energy of the incident radiation is less than the work function of a metal. Reason \(R\) : Kinetic energy of the photoelectrons is zero, if the energy of the incident radiation is equal to the work function of a metal. In the light of the above statements, choose the most appropriate answer from the options given below

A Both \(A\) and \(R\) are correct and \(R\) is the correct explanation of \(A\)
B Both \(A\) and \(R\) are correct but \(R\) is not the correct explanation of \(A\)
C \(A\) is correct but \(R\) is not correct
D \(A\) is not correct but \(R\) is correct

Verified Solution

Answer & Solution

Correct Answer

(B) Both \(A\) and \(R\) are correct but \(R\) is not the correct explanation of \(A\)

Step-by-step Solution

Detailed explanation

To free the electron from metal surface minimum energy required, is equal to the work function of that metal. So Assertion \(A\), is correct. \(h v = w _{0}+ K. E. _{\max }\) if \(h v = w _{0}\) \(\Rightarrow\) \(K.E.\) \(_{\text {max }}=0\) Hence reason \(R\), is correct, But…

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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