Step 1 : Understanding the Question:
The topic of this question is the Photoelectric Effect, a key concept in Modern Physics and the Dual Nature of Radiation and Matter. This phenomenon involves the ejection of electrons from a metal surface when light of a sufficient frequency shines on it. The question provides the "work function" of a metal and asks us to identify which incident photon energy will successfully trigger the release of an electron. It tests the fundamental threshold condition required for the photoelectric effect to take place.
Step 2 : Key Formulas and approach:
We use Einstein’s photoelectric equation to understand the energy balance:
1. Einstein's Equation: $E = \phi_0 + K_{max}$
2. Threshold Condition: For emission to occur, $E \ge \phi_0$.
Where:
- $E$ is the energy of the incident photon.
- $\phi_0$ (Phi) is the work function (the minimum energy required to liberate an electron).
- $K_{max}$ is the maximum kinetic energy of the emitted photoelectron.
Step 3 : Detailed Explanation:
The work function ($\phi_0$) is a constant property of a specific metal. In this case, $\phi_0 = 2\text{ eV}$.
This means every single electron is "bound" to the metal by an energy of at least $2\text{ eV}$. To escape, it must receive at least this much energy from a single incoming photon.
If the incident light energy $E$ is less than $2\text{ eV}$, the electron will not have enough energy to break free from the metal's surface, and no emission will occur, regardless of how intense the light is.
Let's check the options: (A) $1\text{ eV}$ is less than $2\text{ eV}$, so no emission. (B) $1.5\text{ eV}$ is also less than $2\text{ eV}$, so no emission.
Option (C) $2.5\text{ eV}$ is greater than the work function of $2\text{ eV}$. This means the photon has enough energy to liberate the electron ($2\text{ eV}$) and still has some leftover energy ($0.5\text{ eV}$) which becomes the kinetic energy of the moving electron.
Option (D) "2 eV only" is incorrect because any energy equal to OR greater than the work function will cause emission. Emission is not restricted to just the threshold value.
Step 4 : Final Answer:
Since $2.5\text{ eV}$ is the only provided value that exceeds the $2\text{ eV}$ threshold of the work function, it is the only case where photoelectric emission occurs. The correct option is (C).