Statement-1: Kinetic energy of photoelectrons increases with increases in the frequency of incident radiation
Statement-2: The number of photoelectrons ejected increases with increases in intensity of incident radiation.

Options

A. Statement-1 is true, statement-2 is true, statement-2 is a correct explanation for statement-1
B. Statement-1 is true, statement-2 is true, statement-2 is not a correct explanation for statement-1
C. Statement-1 is true, statement-2 is false.
D. Statement-1 is false, statement-2 is true.

Answer

To analyze the statements provided in the question, we can break down the concepts involved:

### Step 1: Understanding Statement-1
**Statement-1**: Kinetic energy of photoelectrons increases with increases in the frequency of incident radiation.

- According to the photoelectric effect, the kinetic energy (KE) of the emitted photoelectrons can be expressed using the equation:

\[ KE = h\nu - \phi \]

where:
- \( KE \) is the kinetic energy of the photoelectron,
- \( h \) is Planck's constant,
- \( \nu \) is the frequency of the incident radiation,
- \( \phi \) is the work function (the minimum energy required to eject an electron from the surface).

- From this equation, we can see that as the frequency (\( \nu \)) of the incident radiation increases, the kinetic energy of the emitted photoelectrons also increases, assuming the work function (\( \phi \)) remains constant.

### Conclusion for Statement-1
- **Statement-1 is true**.

### Step 2: Understanding Statement-2
**Statement-2**: The number of photoelectrons ejected increases with increases in intensity of incident radiation.

- The intensity of the incident radiation is related to the number of photons striking the surface per unit time. Higher intensity means more photons are available to interact with the electrons in the material.

- According to the photoelectric effect, if the energy of the incident photons (which is dependent on frequency) is greater than the work function, more photons will lead to more photoelectrons being emitted. Thus, increasing the intensity of the radiation (while keeping the frequency constant) will indeed increase the number of photoelectrons ejected.

### Conclusion for Statement-2
- **Statement-2 is true**.

### Step 3: Evaluating the Relationship Between the Statements
- While both statements are true, the second statement does not explain the first statement. The kinetic energy of the photoelectrons is related to the frequency of the incident radiation, while the number of photoelectrons is related to the intensity of the radiation.

### Final Conclusion
- The answer to the question is that both statements are true, but Statement-2 does not provide a correct explanation for Statement-1.

### Answer
- The correct option is **b**: Statement-1 is true, Statement-2 is true, but Statement-2 is not a correct explanation of Statement-1.

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