Nuclei - Result Question 27
28. The power obtained in a reactor using $U^{235}$ disintegration is $1000 kW$. The mass decay of $U^{235}$ per hour is
(a) 10 microgram
(b) 20 microgram
(c) 40 microgram
(d) 1 microgram
[2011]
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Answer:
Correct Answer: 28. (c)
Solution:
(c) $E=mc^{2}$
$m=\frac{E}{c^{2}}$
So, mass decay per second $\frac{dm}{dt}=\frac{1}{c^{2}} \frac{dE}{dt}=\frac{1}{c^{2}}$ (Power in watt)
$=\frac{1}{(3 \times 10^{8})^{2}} \times 1000 \times 10^{3}$
and mass decay per hour $=\frac{dm}{dt} \times 60 \times 60$
$=\frac{1}{(3 \times 10^{8})^{2}} \times 10^{6} \times 3600=4 \times 10^{-8} kg$
$=40$ microgram
