The binding energy per nucleon for is approximately

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

Problem

The binding energy per nucleon for

^{235}\text{U}

is approximately

7.6\,\text{MeV}

, while that for the fission fragments with mass number

A=118

is approximately

8.5\,\text{MeV}

. Assume that one

^{235}\text{U}

nucleus splits into two identical fragments of mass number

118

(ignore the small difference in mass number and the energy carried away by emitted neutrons). Take

1\,\text{u}=931\,\text{MeV}/c^{2}

and Avogadro’s number

N_{\!A}=6.02\times10^{23}\,\text{mol}^{-1}

. (i) Calculate the total binding energy of the parent nucleus and of the two fragments. (ii) Hence determine the energy released per fission of one

^{235}\text{U}

nucleus, in MeV. (iii) Estimate the energy released, in joules, by completely fissioning

1\,\text{kg}

^{235}\text{U}