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 \( I \) can be expressed as:
\[ I = \frac{nh\nu}{A}, \] where \( n \) is the number of photons per unit time, \( h \) is Planck’s constant, \( \nu \) is the frequency, and \( A \) is the area. Rearranging for \( n \):
\[ n = \frac{IA}{h\nu}. \] For a constant intensity \( I \), if the frequency \( \nu \) increases, the number of photons \( n \) decreases. Thus, Assertion A is incorrect.

2. **Analysis of Reason R:**
According to the photoelectric effect, the maximum kinetic energy of emitted electrons is given by:
\[ K_{\text{max}} = h\nu - \phi, \] where \( \phi \) is the work function of the material. As frequency \( \nu \) increases, \( K_{\text{max}} \) also increases. Therefore, Reason R is correct.

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