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Question #43632

Difficulty: 8/10 | 🟢 Free

The Question

A photoelectric cell consists of two large parallel planar electrodes in vacuum. The emitter plate is illuminated by monochromatic light of photon energy $E = 6.0 \text{ eV}$ . The work function of the emitter material is $\Phi = 2.0 \text{ eV}$ . A variable voltage source is connected across the electrodes and adjusted to apply a retarding potential difference exactly equal to the stopping potential $V_0$ , such that the photocurrent just drops to zero. The voltage source is then disconnected, leaving the electrodes isolated. Subsequently, the entire gap between the electrodes is filled with a transparent, non-conducting liquid of dielectric constant $\epsilon_r = 4$ . Assuming the work function of the emitter and the incident photon energy remain unchanged, what is the maximum kinetic energy of the first few photoelectrons upon reaching the collector plate?

Options

A.
$3.0 \text{ eV}$
B.
$0 \text{ eV}$
C.
$1.0 \text{ eV}$
D.
$4.0 \text{ eV}$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Stopping Potential Sign|Medium Dependency|Einstein's Photoelectric Equation|Approximations

Why This Question Is Tricky

Common Mistakes

This question tests the intersection of the photoelectric effect and electrostatics.

The lethal trap lies in treating the stopping potential as an intrinsic, immutable property of the incident light and metal surface, rather than a macroscopic electrostatic potential difference required to do work against the electron's kinetic energy.

Students often incorrectly assume that since the light and metal are unchanged, the stopping potential remains $4.0 \text{ V}$ , leading them to choose $0 \text{ eV}$ .

By disconnecting the battery and introducing a dielectric, the actual retarding potential is screened by the medium's polarization ( $V' = V_0/\epsilon_r$ ), lowering the potential barrier and allowing electrons to reach the collector with residual kinetic energy.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Dual Nature of Radiation and Matter - Class 12
Concept	Stopping Potential Sign
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free