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 $3\times {10}^{8}m/s$. The final momentum of the object is:

• A. $0.3\times {10}^{-17}kgm{s}^{-1}$
• B. $1.0\times {10}^{-17}kgm{s}^{-1}$
• C. $3.0\times {10}^{-17}kgm{s}^{-1}$
• D. $9.0\times {10}^{-17}kgm{s}^{-1}$

Answer 1

The correct option is B $1.0\times {10}^{-17}kgm{s}^{-1}$

Sol$.\left(B\right)$
$t=100\times {10}^{-9}sec,P=30\times {10}^{-3}$Watt,

$C=3\times {10}^{8}m/s$

Incident energy $=Pt$

By debroglie wavelength, $\lambda =h/p$

and Energy of photon is $E=hc/\lambda$

From above two equations, $E=pc$

Momentum $p=\frac{Pt}{C}=\frac{30\times {10}^{-3}\times 100\times {10}^{-9}}{3\times {10}^8}=1.0\times {10}^{-17}$ kg ms${}^{-1}$

So, the answer is option (B).