The power obtained in a reactor using ^{235}U | vedclass

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(C) According to Einstein's mass-energy equivalence relation,$E = mc^2$,where $m$ is the mass defect and $E$ is the energy released.The power $P$ is t

Vedclass · Accepted Answer

$40$

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(C) According to Einstein's mass-energy equivalence relation,$E = mc^2$,where $m$ is the mass defect and $E$ is the energy released.The power $P$ is the rate of energy release,$P = \frac{\Delta E}{\Delta t}$.Thus,the rate of mass decay is given by $\frac{\Delta m}{\Delta t} = \frac{P}{c^2}$.Given $P = 1000 	ext{ kW} = 10^6 	ext{ W}$ and $c = 3 	imes 10^8 	ext{ m/s}$.Mass decay per second = $\frac{10^6 	ext{ J/s}}{(3 	imes 10^8 	ext{ m/s})^2} = \frac{10^6}{9 	imes 10^{16}} 	ext{ kg/s} = \frac{1}{9} 	imes 10^{-10} 	ext{ kg/s}$.Mass decay per hour = $\left( \frac{1}{9} 	imes 10^{-10} 	ext{ kg/s} ight) 	imes 3600 	ext{ s} = 400 	imes 10^{-10} 	ext{ kg} = 4 	imes 10^{-8} 	ext{ kg}$.Since $1 	ext{ kg} = 10^9 \mu g$,the mass decay per hour = $4 	imes 10^{-8} 	imes 10^9 \mu g = 40 \mu g$.

The power obtained in a reactor using $^{235}U$ disintegration is $1000 \text{ kW}$. The mass decay of $^{235}U$ per hour is ............ $\mu g$.

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