AIIMS 2006 Physics Photoelectric Effect Assertion Reason Question

To evaluate the given question regarding the photoelectric effect, we need to analyze the Assertion and Reason provided.

Assertion

Assertion: The photoelectrons produced by a monochromatic light beam incident on a metal surface have a spread in their kinetic energies.

Explanation: The photoelectric effect states that when light shines on a metal surface, it can eject electrons (photoelectrons) from that surface. The kinetic energy of these photoelectrons can be calculated using the equation derived from Einstein's photoelectric equation:

$$K.E. = hf - \phi$$

where:

• $K.E.$ is the kinetic energy of the emitted electron,
• $h$ is Planck's constant,
• $f$ is the frequency of the incident light,
• $\phi$ is the work function of the metal (the minimum energy required to remove an electron from the metal surface).

While the frequency $f$ of the incident monochromatic light is constant, the kinetic energy of the emitted photoelectrons can vary due to several factors, including:

1. Different depths from which the electrons are emitted (since electrons emitted from deeper layers may have different energy states).
2. Variations in the electron's binding energy depending on their initial positions within the metal.

Thus, the assertion is true; photoelectrons exhibit a spread in their kinetic energies.

Reason

Reason: The work function of the metal varies as a function of depth from the surface.

Explanation: The reason provided states that the work function $\phi$ varies with depth. While it is true that the work function can vary slightly due to impurities, crystal structure, and other factors, the standard model of the photoelectric effect assumes a uniform work function for simplicity. In most practical cases and basic physics problems, we treat the work function as constant for a specific metal.

Given this understanding, the statement that the work function varies with depth is not commonly accepted in the context of the photoelectric effect as it applies to this situation. Therefore, the reason is false.

Conclusion

• The Assertion is true because photoelectrons emitted by a monochromatic light beam indeed show a spread in kinetic energies.
• The Reason is false as the work function is generally considered constant in basic analysis.

Thus, the correct answer is C) Assertion is true but Reason is false.

Clarifying Other Options

• Option A: Both Assertion and Reason are true, and Reason is the correct explanation of Assertion. (Incorrect, because the Reason is false.)
• Option B: Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion. (Incorrect, because the Reason is false.)
• Option D: Both Assertion and Reason are false. (Incorrect, because the Assertion is true.)

Key Takeaways

• Understand the distinction between the assertion and the reason.
• Recognize that while photoelectron kinetic energy can vary, the work function is often treated as constant in the context of basic photoelectric effect problems.
• Familiarize yourself with the relevant equations, particularly the photoelectric equation, to solve related problems effectively.