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Atoms and Nuclei question

2011 · Q139
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Atoms and Nuclei question

2011 · Q139

NEETPhysicsAtoms and NucleiMCQ+4 / −1
The power obtained in a reactor using U235 disintegration is 1000 kW. The mass decay of U235 per hour is
  1. A
    10 microgram
  2. B
    20 microgram
  3. C
    40 microgram
  4. D
    1 microgram
View written solutionFree

Correct answer: C

From Einstein relation, E = mc2

Rearranging, m = Ec2{E \over {{c^2}}}c2E​

We see that mass decay per second :

dmdt{{dm} \over {dt}}dtdm​ = 1c2{1 \over {{c^2}}}c21​ × dEdt{{dE} \over {dt}}dtdE​ = 1000×103(3×108)2{{1000 \times {{10}^3}} \over {{{\left( {3 \times {{10}^8}} \right)}^2}}}(3×108)21000×103​

Now mass decay of U235 per hour,

= dmdt{{dm} \over {dt}}dtdm​ ×\times× 60 ×\times× 60

= 1000×103(3×108)2{{1000 \times {{10}^3}} \over {{{\left( {3 \times {{10}^8}} \right)}^2}}}(3×108)21000×103​ ×\times× 3600

= 4 × 10–8 kg = 40 microgram

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