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Question #43768

Difficulty: 8/10 | 🟢 Free

The Question

A rigid vacuum phototube of total mass MM is located in deep space (a gravity-free region). Inside the tube, a planar cathode with work function Φ\Phi and a parallel planar anode are separated by a distance dd. A highly intense laser beam of frequency ν\nu (where hν>Φh\nu > \Phi), uniform intensity II, and cross-sectional area AA is incident normally on the perfectly reflecting outer surface of the anode end of the tube. The radiation pressure from the laser accelerates the entire phototube along the axis perpendicular to the electrodes. If mm and −e-e are the mass and charge of an electron respectively, and cc is the speed of light, what is the exact stopping potential VsV_s required to just prevent the most energetic photoelectrons from reaching the anode? (Assume the mass of the emitted electrons is negligible compared to MM).

Options

  • A.

    hν−Φe+2mIAdeMc\frac{h\nu - \Phi}{e} + \frac{2mIAd}{eMc}

  • B.

    hν−Φe−2mIAdeMc\frac{h\nu - \Phi}{e} - \frac{2mIAd}{eMc}

  • C.

    hν−Φe+mIAdeMc\frac{h\nu - \Phi}{e} + \frac{mIAd}{eMc}

  • D.

    hν−Φe\frac{h\nu - \Phi}{e}

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Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

Stopping Potential Sign|Radiation Pressure|Energy Density Locality

Why This Question Is Tricky

Common Mistakes

This question tests the integration of modern physics (the photoelectric effect) with classical mechanics (non-inertial frames and radiation pressure).

The primary trap is treating the photoelectric effect as a purely energetic balance (eVs=hν−ΦeV_s = h\nu - \Phi) while ignoring the macroscopic mechanical state of the system.

Students often fail to recognize that when the apparatus accelerates due to radiation pressure, the electrons inside experience a pseudo-force.

This pseudo-force performs mechanical work on the electrons during their transit, effectively shifting the required electrostatic stopping potential.

Selecting the wrong reference frame or ignoring the external mechanical work done by the radiation field leads directly to the standard, but incorrect, photoelectric equation.

Quick Facts About This Question

Question Information

SubjectPhysics
ChapterDual Nature of Radiation and Matter - Class 12
ConceptStopping Potential Sign
Difficulty8
Cognitive Load7
Target Solve Time160 sec
AccessFree