Question

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Number of photons increases with increase in frequency of light.
Reason (R): Maximum kinetic energy of emitted electrons increases with the frequency of incident radiation.
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 NOT the correct explanation of A.
• B. A is correct but R is not correct.
• C. Both A and R are correct and R is the correct explanation of A.
• D. A is not correct but R is correct.

Answer 1

The Correct Option is D

1. Analysis of Assertion A:
The intensity of light \( I \) is defined as the energy per unit area per unit time. If \( n \) is the number of photons per unit time, then the energy of these photons is \( nhu \). Therefore, \( I = \frac{nhu}{A} \), where \( A \) is the area and \( u \) is the frequency. Rearranging the equation to solve for \( n \):
\[ n = \frac{IA}{hu}. \] For a fixed intensity \( I \), an increase in frequency \( u \) leads to a decrease in the number of photons \( n \). Consequently, Assertion A is incorrect.

2. Analysis of Reason R:
The photoelectric effect equation states that the maximum kinetic energy of emitted electrons is \( K_{\text{max}} = hu - \phi \), where \( h \) is Planck’s constant, \( u \) is the frequency of incident light, and \( \phi \) is the work function of the material. It is evident from this equation that as the frequency \( u \) increases, the maximum kinetic energy \( K_{\text{max}} \) also increases. Thus, Reason R is correct.

Thus, the correct answer is option (4): Assertion A is not correct, but Reason R is correct.