A nuclear reactor generates P = 20 MW power at efficiency η = 60% by nuclear fission of a radio-nuclide whose half life is T = 2.2 years. If each fission releases energy E = 200 MeV, calculate time during which µ = 10 mole of the radionuclide will be consumed completely.
(Avogadro number, N = 6 × 10 23 , log e 2 = 0.693, 1 year = 3.15 × 10 7 s)
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. To operate the nuclear reactor, let the number of fission required per second be n 0 .Then energy released per second by fission reactions = n 0 E
Since, efficiency of the reactor is η , therefore, power output from the reactor = η n 0 E. But it is equal to P therefore, P = η n 0 E or n 0 = 
Let at an instant number of nuclei of radionuclide be n then rate of decay = λ n where λ is decay constant which is equal to 
.
Hence, net rate of decrease of nuclei 
= – λ n + n 0
or 
= – 
= – 
∴ 
= – 
… (1)
At t = 0, number of nuclei are n = µN and time t is to be calculated when all the nuclei are consumed or when n = 0, t = ?
Integrating equation (1) with these limits,
= – 
∴ t = 
log e 
= 10 8 log e (1.0576)s
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems