In the fission of

PHYSICS · Subjective · A Level · Physics · Nuclear physics · Nuclear physics

Problem

In the fission of

^{235}_{\;92}\text U

, about

5\%

of the total energy released is carried away by neutrinos that do not interact with the reactor core, while the remainder appears as useful heat. For a power plant delivering a steady electrical output of

700\,\text{MW}

at an overall efficiency of

35\%

(ratio of electrical power to thermal power produced in the core), answer the following: (a) Calculate the total thermal power that must be produced in the reactor core. (b) Determine the thermal power that must be generated by the fission process before the neutrino loss, i.e., the power corresponding to

100\%

of the fission energy. (c) If the energy actually deposited as heat per fission of

^{235}\text U

(after subtracting the

5\%

neutrino share) is

190\,\text{MeV}

, estimate the number of fissions per second required to maintain the plant at its rated electrical output. (d) Hence find the mass of

^{235}\text U

that undergoes fission in one day of continuous operation. Use

1\,\text{eV}=1.6\times10^{-19}\,\text J

and

N_A = 6.02 \times 10^{23}\,\text{mol}^{-1}

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