The isotopes and are often used as reference points in discussions of nuclear stability

PHYSICS · Subjective · AP · Physics 2: Algebra-based · Modern Physics · Modern Physics

Problem

The isotopes

^{56}\!\text{Fe}

and

^{238}\!\text{U}

are often used as reference points in discussions of nuclear stability. The following atomic mass data are given: • Mass of a proton

=1.007\,276\,\text{u}

• Mass of a neutron

=1.008\,665\,\text{u}

• Nuclear mass of

^{56}\!\text{Fe}=55.934\,94\,\text{u}

• Nuclear mass of

^{238}\!\text{U}=238.050\,79\,\text{u}

•

1\,\text{u}

corresponds to

931.5\,\text{MeV}

of energy. (i) Find the mass defect of one nucleus of

^{56}\!\text{Fe}

. (ii) Calculate the total binding energy of the

^{56}\!\text{Fe}

nucleus. (iii) Repeat parts (i) and (ii) for one nucleus of

^{238}\!\text{U}

. (iv) Determine the binding energy per nucleon for each isotope and state which of the two nuclei is more tightly bound on a per–nucleon basis. (v) If one mole of

^{238}\!\text{U}

nuclei could be completely broken up into fragments whose average binding energy per nucleon equals the value you obtained for

^{56}\!\text{Fe}

, estimate the total energy released in joules. (Take Avogadro number

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

Related theory

Browse the problem library