Question

A large power reactor that has been in operation for some months is turned off, but residual activity in the core still produces 150 MW of power. If the average energy per decay of the fission products is 1.00 MeV, what is the core activity in curies?

$2.53\times 10^{10}\textrm{ Ci}$

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This is College Physics Answers with Shaun Dychko. A nuclear power reactor core has been turned off for a while but it still has a power output of 150 megawatts, which is 150 times 10 to the 6 watts. If we assume that the average energy per decay of the radioactive material that's in the core is 1.00 megaelectron volt per decay, what must be the activity in curies of the core? So we'll convert this megaelectron volts per decay into joules per decay so that's 1.00 times 10 to the 6 electron volts per decay times 1.602 times 10 to the minus 19 joules per electron volt and that is 1.602 times 10 to the minus 13 joules per decay. So the activity is the number of decays per time so that's 1 decay for every 1.602 times 10 to the minus 13 joules and I know I should set up the fraction this way by taking the reciprocal of this because we want to have decays in the numerator of our answer so I am writing this as decays in the top of this fraction per energy and then we multiply by the energy per time— this is watts written as joules per second— and the joules will cancel leaving us with decays per second, which is an activity in units of becquerels but it asks for the decay in units of curies or activity in curies so we multiply by 1 curie for every 3.70 times 10 to the 10 becquerels. All this works out to 2.53 times 10 to the 10 curies.