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Question:

A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 mW and the speed of light is 3×10⁸ m/s. The final momentum of the object is:

0.3×10⁻⁷ kgms⁻¹

1.0×10⁻⁷ kgms⁻¹

3.0×10⁻⁷ kgms⁻¹

9.0×10⁻⁷ kgms⁻¹

Solution:

Sol (B)
t=100×10⁻⁹ sec, P=30×10⁻³ Watt, C=3×10⁸ m/s
Incident energy=Pt
By debroglie wavelength, λ=h/p
and Energy of photon is E=hc/λ
From above two equations, E=pc
Momentump=Pt/C=30×10⁻³×100×10⁻⁹×10⁸=1.0×10⁻⁷ kg ms⁻¹
So, the answer is option (B).