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 a photoelectric experiment, when a negative potential is applied to the anode, it repels photoelectrons. The cut-off voltage (or stopping potential) is the minimum negative potential at which the photoelectric current becomes zero, as it stops even the most energetic photoelectrons. This definition is correct, so Assertion (A) is true. Step 2: Analyze Reason (R).
The threshold frequency \( f_0 \) of a metal is the minimum frequency of incident radiation required to eject photoelectrons, satisfying \( h f_0 = \phi \), where \( \phi \) is the work function. If the frequency \( f<f_0 \), no photoelectrons are emitted. This definition is accurate, so Reason (R) is true. Step 3: Check if Reason (R) explains Assertion (A).
The cut-off voltage \( V_s \) is related to the maximum kinetic energy of photoelectrons: \( e V_s = h f - \phi \), where \( \phi = h f_0 \). The threshold frequency \( f_0 \) defines the condition for photoelectron emission (\( f>f_0 \)), but the cut-off voltage depends on the energy difference \( h f - \phi \), not directly on the definition of threshold frequency. Thus, Reason (R) does not explain Assertion (A). Step 4: Conclusion.
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A), so the correct option is (B).