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Question #43179

Difficulty: 8/10 | 🟢 Free

The Question

A parallel beam of monochromatic light of intensity $I$ and frequency $\nu$ is incident normally on a flat surface. The surface has a reflection coefficient $R$ and a work function $\phi$ (where $h\nu > \phi$ ). Assume that a fraction $R$ of the incident photons are reflected elastically, while the remaining fraction $(1-R)$ are absorbed. Furthermore, assume that every absorbed photon ejects exactly one photoelectron normal to the surface (back towards the light source) with the maximum possible kinetic energy. If $m$ is the mass of an electron, $c$ is the speed of light, and $h$ is Planck's constant, what is the net pressure exerted on the surface?

Options

A.
$\frac{I}{c}(1+R) + \frac{I(1-R)}{h\nu}\sqrt{2m(h\nu - \phi)}$
B.
$\frac{I}{c}(1+R) + \frac{I(1-R)}{h\nu}\sqrt{2mh\nu}$
C.
$\frac{I}{c}(1+R) - \frac{I(1-R)}{h\nu}\sqrt{2m(h\nu - \phi)}$
D.
$\frac{I}{c}(1-R) + \frac{I}{h\nu}\sqrt{2m(h\nu - \phi)}$

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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

Radiation Pressure|Work Function Dependence|Einstein's Photoelectric Equation

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to synthesize classical momentum flux with quantum photoelectric emission.

The primary trap lies in the vector summation of pressures and the energy partition of the absorbed photon.

Students often incorrectly assume that emitted electrons carry away momentum that reduces the net pressure (leading to a negative sign), failing to apply Newton's Third Law which dictates that ejecting mass backwards results in a forward recoil force on the surface.

Additionally, students may neglect the work function $\phi$ when calculating the electron's momentum, erroneously assuming the entire photon energy $h\nu$ converts to kinetic energy, or they may fail to correctly partition the incident intensity $I$ into reflected and absorbed fractions.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Electromagnetic Waves - Class 12
Concept	Radiation Pressure
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free