Question

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Emission of electrons in photoelectric effect can be suppressed by applying a sufficiently negative electron potential to the photoemissive substance. Reason (R) : A negative electric potential, which stops the emission of electrons from the surface of a photoemissive substance, varies linearly with frequency of incident radiation. In the light of the above statements, choose the most appropriate answer from the options given below :

• A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
• B. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
• C. Assertion (A) is true but Reason (R) is false.
• D. Assertion (A) is false but Reason (R) is true.

Answer 1

Answer: (A)

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

Answer 2

Assertion (A) is true because a sufficiently negative potential, known as the stopping potential ($V_s$), creates a retarding electric field that opposes the motion of emitted electrons. If this potential is large enough, it can prevent even the most energetic electrons from reaching the collector, thereby suppressing the photocurrent.

Reason (R) is true. The maximum kinetic energy of the emitted photoelectrons is given by $KE_{max} = h\nu - \phi$, where $h$ is Planck's constant, $\nu$ is the frequency of incident radiation, and $\phi$ is the work function of the photoemissive substance. The stopping potential ($V_s$) is the potential difference required to stop these electrons, so $KE_{max} = eV_s$, where $e$ is the elementary charge. Equating these gives $eV_s = h\nu - \phi$, which can be rearranged to $V_s = \frac{h}{e}\nu - \frac{\phi}{e}$. This equation shows a linear relationship between the stopping potential ($V_s$) and the frequency of incident radiation ($\nu$).

Reason (R) correctly explains Assertion (A) because the linear relationship described in Reason (R) quantifies the negative potential (stopping potential) that suppresses electron emission, providing the physical basis for Assertion (A).