The radioactive isotope 92232U emits alpha particles with an energy of 5.30MeV and has a half life of 74 years. For a sample containing 1.30 * 1024 atoms, calculate the maximum theoretical power output.
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Answer:
Power = decrease in num of radioactive isotopes * 5.3MeV / change in T (in seconds) = -dN/dt * 5.3 MeV
The largest value of dN/dT occurs at N = 1.3 * 1024 since
so, subsitutiting N = 1.3 * 1024, and λ = ln 2 / (74*365*24*3600 s), and 1eV = 1.602* 10-19 W,
Maximum theoretical power output = λN * 5.3 * 1.602* 10-19
Maximum theoretical power output = 330W
