Question

Assertion (A): On increasing the intensity of incident light of frequency \( v(> v_0) \) on a photosensitive surface, the photocurrent increases. Reason (R): The stopping potential for a photosensitive surface increases with increase of frequency \( v(> v_0) \) of incident light.

• A. Both A and R are true and R explains A
• B. Both A and R are true but R does not explain A
• C. A is true but R is false
• D. A is false and R is false

Hint:

Intensity controls the number of emitted electrons and hence photocurrent. Frequency controls the energy of emitted electrons and hence stopping potential.

Answer 1

The Correct Option is B

Concept: According to Einstein's photoelectric equation, \[ h\nu=\phi+K_{\max} \] or \[ K_{\max}=h\nu-\phi. \] The photoelectric effect depends mainly on two parameters:
• Intensity of incident light
• Frequency of incident light The intensity of light determines the number of photons incident per second, whereas the frequency determines the energy carried by each photon. Assertion Analysis: The given frequency satisfies \[ \nu>\nu_0, \] where \(\nu_0\) is the threshold frequency of the photosensitive surface. Therefore photoemission takes place. When the intensity of incident light is increased while keeping the frequency unchanged, a larger number of photons strike the metal surface per unit time. As a result, a greater number of electrons are emitted from the surface every second. Since photocurrent is directly proportional to the number of photoelectrons reaching the collector, \[ \text{Photocurrent} \propto \text{Number of emitted electrons}. \] Hence increasing intensity increases the photocurrent. Therefore, the Assertion is TRUE. Reason Analysis: The stopping potential \(V_0\) is related to the maximum kinetic energy of emitted photoelectrons by \[ eV_0=K_{\max}. \] Using Einstein's equation, \[ eV_0=h\nu-\phi. \] This equation clearly shows that the stopping potential depends on the frequency of the incident radiation. As the frequency increases above the threshold frequency, \[ h\nu-\phi \] increases and therefore the stopping potential also increases. Hence the Reason is also TRUE. Relationship Between Assertion and Reason: The Assertion talks about the increase in photocurrent due to increase in intensity. The Reason talks about increase in stopping potential due to increase in frequency. These are two different aspects of the photoelectric effect. \[ \text{Intensity} \longrightarrow \text{Photocurrent} \] whereas \[ \text{Frequency} \longrightarrow \text{Kinetic Energy and Stopping Potential}. \] Thus, although both statements are individually true, the Reason does not explain the Assertion. Final Answer: \[ \boxed{(B)} \]