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Question #42045

Difficulty: 8/10 | 🟢 Free

The Question

A collimated light source, in its own rest frame, emits $N_0$ photons per second, each of frequency $\nu_0$ . The source moves directly towards a stationary metal plate with a constant speed $v = \frac{3}{5}c$ (where $c$ is the speed of light). The metal plate has a work function $\phi = \frac{1}{2}h\nu_0$ . Assuming all emitted photons strike the plate and the photoelectric quantum efficiency is $\eta$ (electrons emitted per incident photon), what is the stopping potential $V_s$ and the saturation photocurrent $I_s$ measured by an observer at rest with respect to the plate?

Options

A.
$V_s = \frac{3h\nu_0}{2e}, \ I_s = 2\eta e N_0$
B.
$V_s = \frac{3h\nu_0}{2e}, \ I_s = \eta e N_0$
C.
$V_s = \frac{h\nu_0}{2e}, \ I_s = \frac{4}{5}\eta e N_0$
D.
$V_s = \frac{h\nu_0}{2e}, \ I_s = \eta e N_0$

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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

Relative Velocity in 1D|Einstein's Photoelectric Equation|Intensity and Photon Flux

Why This Question Is Tricky

Common Mistakes

This question tests the simultaneous application of the Relativistic Doppler Effect to both photon energy and photon flux.

A common trap is correctly calculating the Doppler-shifted frequency for the stopping potential but failing to realize that the photon arrival rate (flux) is also scaled by the exact same Doppler factor due to time dilation and the changing source-observer distance.

Students often incorrectly assume the saturation current remains $\eta e N_0$ or only apply the Lorentz factor $\gamma$ to the rate, ignoring the relative velocity's effect on the spatial separation of photons.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Motion in a Straight Line - Class 11 Part 1
Concept	Relative Velocity in 1D
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free