Question

Assertion (A): The minimum negative potential applied to the anode in a photoelectric experiment at which photoelectric current becomes zero, is called cut-off voltage.
Reason (R): The threshold frequency for a metal is the minimum frequency of incident radiation below which emission of photoelectrons does not take place.

• A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
• B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
• C. Assertion (A) is true, but Reason (R) is false.
• D. Both Assertion (A) and Reason (R) are false.

Hint:

The cut-off voltage in a photoelectric experiment stops the current by countering the kinetic energy of photoelectrons (\( e V_s = h f - \phi \)). The threshold frequency sets the condition for emission but doesn’t directly explain the stopping mechanism.

Answer 1

The Correct Option is B

Step 1: Analyze Assertion (A).
In the photoelectric effect, a negative potential on the anode repels photoelectrons. The cut-off voltage (stopping potential) is the minimum negative voltage that stops all photoelectrons, making the photoelectric current zero. This is a correct definition, hence Assertion (A) is true.Step 2: Analyze Reason (R).
The threshold frequency \( f_0 \) is the minimum frequency of incident light needed to emit photoelectrons from a metal, defined by \( h f_0 = \phi \), where \( \phi \) is the work function. If the incident frequency \( f \) is less than \( f_0 \), no photoelectrons are emitted. This definition is correct, hence Reason (R) is true.Step 3: Determine if Reason (R) explains Assertion (A).
The cut-off voltage \( V_s \) relates to the maximum kinetic energy of photoelectrons by \( e V_s = h f - \phi \), with \( \phi = h f_0 \). While the threshold frequency \( f_0 \) sets the condition for emission (\( f>f_0 \)), the cut-off voltage is determined by the energy difference \( h f - \phi \), not directly by the definition of threshold frequency itself. Therefore, Reason (R) does not explain Assertion (A).Step 4: Conclusion.
Both Assertion (A) and Reason (R) are true statements. However, Reason (R) does not provide a correct explanation for Assertion (A). The correct option is (B).