Question

Given below are two statements: one is labelled as Assertion (A) and the other one is labelled as Reason (R). 

Assertion (A): Emission of electrons in the 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 the frequency of incident radiation.

In light of the above statements, choose the most appropriate answer from the options given below:

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

Hint:

In photoelectric effect, the stopping potential depends on the energy of incident photons, which in turn depends on the frequency of the radiation, but the relationship is not necessarily linear.

Answer 1

The Correct Option is A

Analysis of Assertion (A) and Reason (R):

Assertion (A): The statement claims that the emission of electrons in the photoelectric effect can be inhibited by applying a sufficiently negative electric potential to the photoemissive material. This is true because applying a negative potential, known as the stopping or retarding potential, counteracts the forward motion of the photo-emitted electrons, preventing them from reaching the anode.

Reason (R): The reason states that the negative electric potential required to stop the emission of electrons from the surface of a photoemissive substance varies linearly with the frequency of incident radiation. This is also correct. According to the photoelectric effect, the stopping potential \(V_0\) is related to the frequency \(ν\) of the incident radiation by the equation \(eV_0 = hν - φ\), where \(e\) is the electron charge, \(h\) is Planck's constant, and \(φ\) is the work function of the material. This equation indeed shows a linear relationship between the stopping potential and frequency.

Thus, both Assertion (A) and Reason (R) are true. However, while (R) is true and states a concept related to the photoelectric effect, it does not directly explain why applying a negative potential suppresses electron emission described in (A). The suppression is primarily due to the opposing electric field, not specifically because of the linear relationship with frequency.

Conclusion:

The correct answer is: Both (A) and (R) are true but (R) is not the correct explanation of (A).

Answer 2

Step 1: Understand the Assertion (A) and Reason (R).
Assertion (A): Emission of electrons in the photoelectric effect can be suppressed by applying a sufficiently negative 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 the frequency of incident radiation.

Step 2: Analyze Assertion (A).
In the photoelectric effect, when light of sufficient frequency falls on a metal surface, electrons are emitted. These emitted electrons can be stopped by applying a retarding (negative) potential to the collector plate. When the applied negative potential equals the maximum kinetic energy of the emitted electrons (called the stopping potential), the emission current becomes zero. Hence, it is true that a sufficiently negative potential can suppress the emission of electrons.

Step 3: Analyze Reason (R).
The stopping potential \( V_0 \) is related to the frequency \( \nu \) of incident light as:
\[ eV_0 = h\nu - \phi, \] where \( \phi \) is the work function of the metal and \( h \) is Planck’s constant.
This shows that the stopping potential \( V_0 \) varies linearly with the frequency \( \nu \). Thus, the reason (R) is also a true statement.

Step 4: Check the connection between (A) and (R).
While both statements are true, the reason (R) does not correctly explain the assertion (A). The assertion is about how applying a negative potential can stop electron emission, while the reason describes how the stopping potential depends on frequency, which is a different concept.

Final Answer:
Both (A) and (R) are true but (R) is not the correct explanation of (A).