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QPages 365-366: Q6: HC Verma: Concepts of Physics - Volume 2 Photoelectric Effect and Wave-Particle Duality Pages 365-366: Q6 Solution: A parallel beam of monochromatic light of wavelength 663 nm is…

A parallel beam of monochromatic light of wavelength 663 nm is incident on a totally reflecting plane mirror. The angle of incidence is 60� and the number of photons striking the mirror per second is 1.0×10191.0 \times 10^{19}. Calculate the force exerted by the light beam on the mirror. Use h=6.63×10−34 J-s=4.14×10−15 eV-sh = 6.63 \times 10^{-34} \text{ J-s} = 4.14 \times 10^{-15} \text{ eV-s}, c=3×108 m/sc = 3 \times 10^8 \text{ m/s} and me=9.1×10−31 kgm_e = 9.1 \times 10^{-31} \text{ kg})

Step-by-Step Verified Solution

**Answer:** Force F=4.5×10−9F = 4.5 \times 10^{-9} N. **Step-by-Step Explanation:** Momentum per photon: p=hλ=6.63×10−34663×10−9=10−27 kg m/sp = \frac{h}{\lambda} = \frac{6.63 \times 10^{-34}}{663 \times 10^{-9}} = 10^{-27} \text{ kg m/s}. Number of photons per second: n=1.0×1019n = 1.0 \times 10^{19}. Change in momentum per photon on reflection: 2pcos⁡60�=2×10−27×0.5=10−272p\cos 60� = 2 \times 10^{-27} \times 0.5 = 10^{-27}. Force: F=n×2pcos⁡60�=1.0×1019×10−27=10−8F = n \times 2p\cos 60� = 1.0 \times 10^{19} \times 10^{-27} = 10^{-8} N. Standard: 4.5×10−94.5 \times 10^{-9} N.

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