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A radiation of wavelength 200 \mathrm{~nm} is propagation in the form of a parallel plate surface. The intensity of the beam is 5 \mathrm{~mW} and cross-sectional area is 1.0 \mathrm{~mm}^2. The pressure exerted by radiation on the metallic surface (if the radiation is completely reflected) is:

Option: 1

1.11 \times 10^{-5} \mathrm{~N} / \mathrm{m}^2


Option: 2

3.33 \times 10^{-5} \mathrm{~N} / \mathrm{m}^2


Option: 3

2.22 \times 10^{-5} \mathrm{~N} / \mathrm{m}^2


Option: 4

4.44 \times 10^{-5} \mathrm{~N} / \mathrm{m}^2


Answers (1)

best_answer

The energy of one photon is E=\frac{h c}{\lambda}.

If the power of source is p, the number of photon incident per second on the metallic surface is
N=\frac{p}{E}=\frac{p \lambda}{h c} \text {. }
Momentum of incident photon =\frac{h}{\lambda}.

Change in momentum due to reflection
=\frac{2 h}{\lambda} \text {. }

Total momentum imparted to the surface per second is \frac{2 h}{\lambda} \cdot \frac{\lambda P}{h c}=\frac{2 P}{c}.

Pressure \begin{aligned} =\frac{F}{A}=\frac{2 P / C}{A}=\frac{2 P}{A C} . \\ \end{aligned}

=\frac{2 \times 5 \times 10^{-3}}{3 \times 10^8 \times 10^{-6}}=3.33 \times 10^{-5} \mathrm{~N}^2 \mathrm{~m}^2

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