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): Increasing the intensity of incident light in the photoelectric effect leads to an increase in stopping potential.

Reason (R): An increase in light intensity, provided its frequency exceeds the threshold frequency, results in a higher rate of photoelectron emission.

Concept Used:

Einstein’s photoelectric equation defines the photoelectric effect:

\[ K_{\text{max}} = hu - \phi \]

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

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

Step-by-Step Solution:

Step 1: Examine the relationship between intensity and stopping potential.

The equation \( eV_0 = hu - \phi \) shows that stopping potential is determined solely by the frequency \( u \) of the incident light, not its intensity. Consequently, increasing light intensity does not affect stopping potential; it remains constant if the frequency is unchanged.

Step 2: Evaluate Reason (R).

An increase in light intensity means more photons per second strike the metal surface. If each photon possesses energy greater than the work function (\( hu > \phi \)), a greater number of electrons are emitted per unit time. Thus, the rate of photoelectron emission is directly proportional to the intensity of light.

Step 3: Determine the validity of A and R.

• Assertion (A) is false because stopping potential is independent of intensity.
• Reason (R) is true as intensity influences the rate of emission, not the kinetic energy of photoelectrons.

Final Computation & Result:

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