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Question #43604

Difficulty: 8/10 | 🟢 Free

The Question

In a photoelectric experiment, a planar metal emitter plate with work function $\Phi$ is located at $x = 0$ and a parallel collector plate is located at $x = d$ . The emitter is illuminated by monochromatic light of wavelength $\lambda$ . The region between the plates contains a non-uniform static electric field given by $\vec{E} = E_0 \left(1 - \frac{3x}{2d}\right) \hat{i}$ , where $E_0$ is a positive constant. Assuming the photons are neutral and unaffected by the electric field, what is the minimum value of $E_0$ required to completely stop the photocurrent? (Here $e$ is the elementary charge, $h$ is Planck's constant, and $c$ is the speed of light. Assume $\frac{hc}{\lambda} > \Phi$ ).

Options

A.
$\frac{3}{ed} \left( \frac{hc}{\lambda} - \Phi \right)$
B.
$\frac{4}{ed} \left( \frac{hc}{\lambda} - \Phi \right)$
C.
$\frac{2}{ed} \left( \frac{hc}{\lambda} - \Phi \right)$
D.
$\frac{1}{ed} \left( \frac{hc}{\lambda} - \Phi \right)$

Check Your Answer

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

Photon Neutrality|Stopping Potential Sign|Non-Uniform Acceleration Constraint

Why This Question Is Tricky

Common Mistakes

This question tests the application of the Work-Energy Theorem in a non-uniform electric field within a photoelectric setup.

The primary trap exploits the student's reliance on the standard stopping potential formula ( $eV_s = K_{max}$ ), where $V_s$ is assumed to be the potential difference strictly between the emitter and collector plates.

By introducing a non-uniform field that creates a potential energy maximum between the plates (at $x = 2d/3$ ), the actual stopping barrier is higher than the endpoint potential difference.

Students who blindly integrate the field from $x=0$ to $x=d$ will incorrectly calculate the required field based on the net potential difference, failing to recognize that electrons are reflected back before even reaching the collector.

Quick Facts About This Question

Question Information

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