Correct Option: (b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Step 1 (Governing Law & Principle): [0.25 Mark]
The photoelectric effect is governed by Einstein's Photoelectric Equation:
$$K_{max} = h\nu - \Phi_0$$Where $K_{max}$ is the maximum kinetic energy, $h\nu$ is the energy of the incident photon, and $\Phi_0$ is the work function of the metal.
Step 2 (Step-by-Step Logical Deduction): [0.50 Mark]
- Analysis of (A): When photons strike the metal surface, some electrons are emitted from the surface (requiring only $\Phi_0$), while others are emitted from deeper layers. Electrons from deeper layers lose energy due to collisions before reaching the surface, resulting in a range of kinetic energies from $0$ to $K_{max}$. Thus, Assertion (A) is True.
- Analysis of (R): The work function $\Phi_0$ is indeed a characteristic property of a metal representing the minimum energy required to eject an electron. Thus, Reason (R) is True.
- Correlation: While both statements are scientifically accurate, the range of speeds (Assertion) is due to the inelastic collisions of electrons within the metal lattice, not merely the existence of a work function. Therefore, (R) is not the correct explanation for (A).
Step 3 (Final Concluded Answer): [0.25 Mark]
Since both statements are independently correct but the reason does not explain the cause of the energy distribution, the correct choice is (b).
💡 EL10 Concept Insight: Think of the metal like a crowded room; the electrons at the surface can leave easily, but those buried deep inside bump into other atoms and lose energy on their way out, which is why they come out at different speeds!