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.**

Answer 2

Step 1: Recall the relationship between energy, frequency, and photons
Each photon of light carries energy given by the equation:
\[ E = h\nu \] where \(E\) is the energy of one photon, \(h\) is Planck’s constant, and \(\nu\) is the frequency of the light. This means that as the frequency increases, the energy per photon increases, not the number of photons.

Step 2: Examine the Assertion (A)
Assertion (A): “Number of photons increases with increase in frequency of light.”
This statement is incorrect because the number of photons depends on the total energy or intensity of the light source, not on its frequency. For a given intensity, if frequency increases, each photon carries more energy, so the total number of photons actually decreases. Hence, A is false.

Step 3: Examine the Reason (R)
Reason (R): “Maximum kinetic energy of emitted electrons increases with the frequency of incident radiation.”
This statement is correct. According to Einstein’s photoelectric equation:
\[ K_{\text{max}} = h\nu - \phi \] where \(\phi\) is the work function of the metal. As frequency \(\nu\) increases, \(h\nu\) increases, and thus \(K_{\text{max}}\) (the maximum kinetic energy of photoelectrons) increases linearly with frequency. So, R is true.

Step 4: Check the logical connection between A and R
Although R is a true statement, it does not explain A because the kinetic energy of electrons is not related to the number of photons but to the energy of each photon. Therefore, the reason R is correct, but it does not justify A.

Final Answer:

A is not correct but R is correct.