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The power obtained in a reactor using $U^{235}$ disintegration is 1000 kW. The mass decay of $U^{235}$ per hour is
A
1 microgram
B
10 microgram
C
20 microgram
D
40 microgram
Detailed Solution
Energy produced in one hour: $E = P\times t = 1000\times10^3\ W\times3600\ s = 3.6\times10^9$ J
By mass–energy equivalence, $E = mc^2$
$m = \frac{E}{c^2} = \frac{3.6\times10^9}{(3\times10^8)^2} = \frac{3.6\times10^9}{9\times10^{16}}$
$m = 4\times10^{-8}$ kg
$m = 4\times10^{-5}$ g = 40 microgram
By mass–energy equivalence, $E = mc^2$
$m = \frac{E}{c^2} = \frac{3.6\times10^9}{(3\times10^8)^2} = \frac{3.6\times10^9}{9\times10^{16}}$
$m = 4\times10^{-8}$ kg
$m = 4\times10^{-5}$ g = 40 microgram