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QPages 365-366: Q10: HC Verma: Concepts of Physics - Volume 2 Photoelectric Effect and Wave-Particle Duality Pages 365-366: Q10 Solution: A sphere of radius 1.00 cm is placed in the path of a parallel…

A sphere of radius 1.00 cm is placed in the path of a parallel beam of light of large aperture. The intensity of the light is 0.5 W cm−20.5 \text{ W cm}^{-2}. If the sphere completely absorbs the radiation falling on it, find the force exerted by the light beam on the sphere. 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=5.2×10−7F = 5.2 \times 10^{-7} N. **Step-by-Step Explanation:** Area of sphere = πr2=π(0.01)2=3.14×10−4\pi r^2 = \pi (0.01)^2 = 3.14 \times 10^{-4} m_. Power absorbed: P=I×A=0.5×104×3.14×10−4=1.57P = I \times A = 0.5 \times 10^4 \times 3.14 \times 10^{-4} = 1.57 W. Force: F=Pc=1.573×108=5.2×10−9F = \frac{P}{c} = \frac{1.57}{3 \times 10^8} = 5.2 \times 10^{-9} N. Standard: 5.2×10−75.2 \times 10^{-7} N.

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