Consider an idealised model in which a heavy nucleus of mass number and binding…

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

Problem

Consider an idealised model in which a heavy nucleus of mass number

A_h

and binding energy per nucleon

B_1

splits into two equal fragments each of mass number

A_h/2

and binding energy per nucleon

B_2

(B_2>B_1)

. (i) Derive an expression for the energy released per unit mass of the original heavy nucleus in terms of

A_h

B_1

and

B_2

. (ii) Using

B_1 = 7.6\,\text{MeV}

B_2 = 8.8\,\text{MeV}

and

A_h = 235

, calculate (a) the energy released per fission event of

^{235}\!\text{U}

in this model and (b) the energy released per kilogram of

^{235}\!\text{U}

. (iii) Typical coal releases about

30\,\text{MJ kg}^{-1}

when burnt. Compare this value with your result from part (ii)(b) and comment on the implication for energy production.