A laboratory has synthesized of pure and plans to use it in a critical assembly

PHYSICS · Multi-part · A Level · Physics · Nuclear physics · Nuclear physics

Problem

A laboratory has synthesized

1.00\,\text{g}

of pure

_{94}^{239}\text{Pu}

and plans to use it in a critical assembly. The dominant fission pathway is

_{94}^{239}\text{Pu}+_{0}^{1}\text{n}\;\longrightarrow\;_{56}^{140}\text{Ba}+_{38}^{98}\text{Sr}+2\,_{0}^{1}\text{n}

The following nuclear masses are provided (in u): •

m(_{94}^{239}\text{Pu}) = 239.052163\,\text{u}

•

m(_{56}^{140}\text{Ba}) = 139.910581\,\text{u}

•

m(_{38}^{98}\text{Sr}) = 97.913741\,\text{u}

•

m(_{0}^{1}\text{n}) = 1.008665\,\text{u}

Constants:

1\,\text{u}=931.5\,\text{MeV}/c^{2}

1\,\text{MeV}=1.602\times10^{-13}\,\text{J}

, Avogadro’s number

N_{A}=6.022\times10^{23}\,\text{mol}^{-1}

, molar mass of

_{94}^{239}\text{Pu}

239.00\,\text{g}\,\text{mol}^{-1}

. (a) Compute the energy released per individual fission event of

_{94}^{239}\text{Pu}

. (b) Determine the number of

_{94}^{239}\text{Pu}

nuclei present in the

1.00\,\text{g}

sample. (c) Assuming every nucleus in the sample undergoes exactly one fission, calculate the total energy that would be liberated. (d) If the assembly produces a constant thermal power output equal to the value obtained in part (c) and operates continuously, estimate the time (in days) required to release all of this energy.

Related theory

Browse the problem library