An aneutronic fusion scheme burns deuterium with helium-3: ^ 2 H + ^ 3 He ^ 4 He + ^ 1 H

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Nuclear Physics · Relativistic dynamics and fields in flat spacetime

Relativity and Gravitation, Ch Mass as energy: binding, defect and annihilation

Problem

An aneutronic fusion scheme burns deuterium with helium-3:

^{2}\mathrm{H} + {}^{3}\mathrm{He} \to {}^{4}\mathrm{He} + {}^{1}\mathrm{H}.

Neutral-atom masses:

^{2}\mathrm{H}

2.014102\ \mathrm{u}

;

^{3}\mathrm{He}

3.016029\ \mathrm{u}

;

^{4}\mathrm{He}

4.002603\ \mathrm{u}

;

^{1}\mathrm{H}

1.007825\ \mathrm{u}

. Take

1\ \mathrm{u}\,c^2 = 931.494\ \mathrm{MeV}

. A student reasons: “A helium-4 nucleus is made, and its binding energy is

28.30\ \mathrm{MeV}

, so

28.30\ \mathrm{MeV}

is released per reaction.” ((a)) Show that the electrons balance, so that neutral-atom masses may be used, and compute the energy released

Q

in MeV. ((b)) Say in one or two sentences what is wrong with the student's reasoning.