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?

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Considering the given information:

Power produced by the reactor

\(P = 150\,{\rm{MW}}\)

Average energy per decay

\(E = 1.00\,\,{\rm{MeV}}\)

Apply the formula:

Thecore'sactivityRisgivenby,

\(R = \frac{p}{E}\)

Injoules,expresstheenergyperdecay.

\(\begin{align}{}E & = & 1.00\,{\rm{MeV}} \times \frac{{1.6 \times {{10}^{ - 13}}\;{\rm{J}}}}{{1\,{\rm{MeV}}}}\\ & = & 1.6 \times {10^{ - 13}}{\rm{\;J}}\end{align}\)

Calculatethecore'sactivity.

\(\begin{align}{}R & = & \frac{p}{E}\\ & = & \frac{{150 \times {{10}^6}\,{\rm{W}}}}{{1.6 \times {{10}^{ - 13}}\;{\rm{J}}}}\\ & = & 9.375 \times {10^{20}}{\rm{ decays/s}}\end{align}\)

Curie can be used to express activity.

\(\begin{align}{}R & = & \left( {9.375 \times {{10}^{20}}{\rm{ decays/s}}} \right)\left( {\frac{{1\,Ci}}{{3.7 \times {{10}^{10}}{\rm{ decays/s }}}}} \right)\\ & = & 2.533 \times {10^{10}}\,Ci\end{align}\)

Therefore, the required core activity of the large power reactor with residual activity that produces a power of 150 MW of power is \(2.533 \times {10^{10}}\,Ci\).