Question Analysis: Assertion-Reasoning Type (1 Mark)
Step 1 (Conceptual Definition of Assertion): [0.5 Mark]
The Assertion states that the minimum negative potential applied to the anode at which photoelectric current becomes zero is the cut-off voltage (or stopping potential, $V_0$). According to the photoelectric effect, the kinetic energy of the most energetic photoelectrons is given by:
$$K_{max} = e V_0$$This definition is scientifically accurate as per NCERT standards.
Step 2 (Conceptual Definition of Reason): [0.5 Mark]
The Reason states that the threshold frequency ($\nu_0$) is the minimum frequency of incident radiation below which no emission occurs. This is the fundamental law of the photoelectric effect, governed by the work function ($\Phi_0$):
$$\Phi_0 = h \nu_0$$Where $h$ is Planck's constant. If $\nu < \nu_0$, the energy of the incident photon is insufficient to overcome the work function of the metal surface.
Step 3 (Final Concluded Answer): [1 Mark]
Correct Option: (b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
- Justification: Both statements are individually correct definitions in the context of the Dual Nature of Radiation and Matter. However, the Reason (threshold frequency) explains the condition for emission, whereas the Assertion (cut-off voltage) explains the stopping of current for already emitted electrons. Thus, (R) does not explain (A).
💡 EL10 Concept Insight:
Think of the threshold frequency as the "entry ticket" price needed to get electrons out of the metal, while the cut-off voltage is like a "bouncing wall" that pushes the already-escaped electrons back to the metal so they can't reach the other side to create a current.