A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the…

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 ms-1. The final momentum of the object is
  1. $0.3 \times 1^{0^{-17}} \, \text{kg m}^{-1}$
  2. $1.0 \times 1^{0^{-17}} \, \text{kg} \, m^{-1}$
  3. $3.0 \times 10^{-17} \, \text{kg m s}^{-1}$
  4. $9.0 \times 10^{-17} \, \text{kg m}^{-1}$

Solution

$ \text{Power} = $\frac{E}{t}$ \quad E = \text{Energy} $ $ \therefore \quad E = \text{Power} \times \text{time} = \frac{hc}{\lambda} $ $ \frac{hc}{\lambda} = 30 \times 10^{-3} \times 100 \times 10^{-9} $ $ \therefore \quad p = \frac{h}{\lambda} = \frac{3 \times 10^{-9}}{3 \times 10^{8}} = 1 \times 10^{-17} \quad kg \, ms $

Asked in: JEE Advanced 2013 (Paper 1)

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