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JEE MAIN - Physics (2025 - 4th April Morning Shift - No. 19)

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason $\mathbf{R}$

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.

In the light of the above statements, choose the correct answer from the options given below

Both $\mathbf{A}$ and $\mathbf{R}$ are true and $\mathbf{R}$ is the correct explanation of $\mathbf{A}$
$\mathbf{A}$ is false but $\mathbf{R}$ is true
Both $\mathbf{A}$ and $\mathbf{R}$ are true but $\mathbf{R}$ is NOT the correct explanation of $\mathbf{A}$
$\mathbf{A}$ is true but $\mathbf{R}$ is false

Explanation

In the photoelectric effect, the stopping potential ($V_s$) is determined by the equation:

$ V_s = \frac{hv - \phi}{e} $

where $ h $ is Planck's constant, $ v $ is the frequency of the incident light, $ \phi $ is the work function of the material, and $ e $ is the charge of the electron. This shows that the stopping potential depends on the frequency of the incident light and the work function, not on the intensity of the light.

The intensity of light ($ I $) affects the number of photons hitting the surface per second, given by:

$ I = \frac{\eta hv}{A} $

where $ \eta $ is the efficiency of photoelectron emission and $ A $ is the area. Increasing the intensity increases the number of photons per second ($ n $), which in turn increases the number of emitted electrons. However, the stopping potential remains unaffected by changes in intensity; it is solely influenced by the frequency of the incident light relative to the work function of the material.

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