Question

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: In photoelectric effect, on increasing the intensity of incident light the stopping potential increases. Reason R: Increase in intensity of light increases the rate of photoelectrons emitted, provided the frequency of incident light is greater than threshold frequency.

• A. Both $\mathbf{A}$ and $\mathbf{R}$ are true but $\mathbf{R}$ is NOT the correct explanation of $\mathbf{A}$
• B. $\mathbf{A}$ is false but $\mathbf{R}$ is true
• C. $\mathbf{A}$ is true but $\mathbf{R}$ is false
• D. Both $\mathbf{A}$ and $\mathbf{R}$ are true and $\mathbf{R}$ is the correct explanation of $\mathbf{A}$

Hint:

The stopping potential in the photoelectric effect does not depend on the intensity of light.

Answer 1

The Correct Option is B

Assertion (A): In photoelectric effect, on increasing the intensity of incident light, the stopping potential increases.

Reason (R): Increase in intensity of light increases the rate of photoelectrons emitted, provided the frequency of incident light is greater than the threshold frequency.

Concept Used:

The photoelectric effect is governed by Einstein’s photoelectric equation:

\[ K_{\text{max}} = h\nu - \phi \]

where \( K_{\text{max}} \) is the maximum kinetic energy of emitted photoelectrons, \( h \) is Planck’s constant, \( \nu \) is the frequency of the incident light, and \( \phi \) is the work function of the metal. The stopping potential \( V_0 \) is related to \( K_{\text{max}} \) as:

\[ eV_0 = K_{\text{max}} = h\nu - \phi \]

Step-by-Step Solution:

Step 1: Analyze the effect of intensity on stopping potential.

From the equation \( eV_0 = h\nu - \phi \), we see that stopping potential depends only on the frequency \( \nu \) of the incident light, not on its intensity. Therefore, increasing the intensity of light does not increase the stopping potential. The stopping potential remains the same if the frequency is unchanged.

Step 2: Analyze the Reason (R).

When the intensity of light increases, the number of photons incident per second on the metal surface increases. If each photon has energy greater than the work function (\( h\nu > \phi \)), more electrons are emitted per unit time. Hence, the rate of photoelectron emission increases with intensity.

Step 3: Evaluate the truth of A and R.

• Assertion (A) is false — stopping potential does not depend on intensity.
• Reason (R) is true — intensity affects the rate of emission, not the energy of photoelectrons.

Final Computation & Result:

Final Answer: Assertion (A) is false, but Reason (R) is true.