Thermonuclear Fusion: The Basic Process — Question 1

Question 1

Balanced atomic masses give the energy of deuterium-tritium fusion

For $^2\mathrm H+{}^3\mathrm H\to{}^4\mathrm{He}+n$, use atomic masses 2.014102 u, 3.016049 u, 4.002603 u and neutron mass 1.008665 u. Use $1\,\mathrm u c^2=931.5$ MeV.

1. Check nucleon and charge conservation and explain why these atomic masses may be used.

2. Find the Q value and the fraction of reactant rest energy released.

Question 1 - Solution

Balanced atomic masses give the energy of deuterium-tritium fusion

(a) Method and calculation

$$A:\ 2+3=4+1,\quad Z:\ 1+1=2+0;\quad\boxed{N_{e,i}=N_{e,f}=2}.$$$$\Delta m=2.014102+3.016049-4.002603-1.008665=.018883\,\mathrm u.$$

(b) Interpretation and further calculation

$$\boxed{Q=.018883(931.5)=17.5895\,\mathrm{MeV}}.$$$$\boxed{\Delta m/(m_D+m_T)=.018883/5.030151=.0037540}.$$

Physical check

Atomic electrons cancel in the mass balance to the stated nuclear-energy precision. A positive Q does not eliminate Coulomb suppression of the collision.