Question

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

• A. $10$ microgram
• B. $20$ microgram
• C. $40$ microgram
• D. $1$ microgram

Answer 1

The correct option is C $40$ microgram

$E=m{c}^2$
$m=\frac{E}{c^2}$
So mass decay per second, $\frac{dm}{dt}=\frac{1}{c^2}\frac{dE}{dt}=\frac{1}{c^2}$ (Power in watt)
$=\frac{1}{3\times {10}^{8^2}}\times 1000\times {10}^3$
Mass decay per hour $=\frac{dm}{dt}\times 60\times 60$

$=\frac{1}{3\times {10}^{8^2}}\times {10}^6\times 3600=4\times {10}^{-8}kg$
$=40microgram$