Thermonuclear Fusion: The Basic Process — Question 9

Question 9

Energy per reacting nucleon differs from energy per reaction

Compare ideal D-T fusion releasing 17.6 MeV per 5 reacting nucleons with an illustrative fission event releasing 200 MeV per 236 reacting nucleons. Ignore small nucleon-mass differences.

1. Compare released energy per event and per reacting nucleon.

2. Find the ratio of ideal energy release per equal reactant mass, and explain why it does not directly compare power-plant outputs.

Question 9 - Solution

Energy per reacting nucleon differs from energy per reaction

(a) Method and calculation

$$\boxed{Q_f/Q_{\mathrm{DT}}=200/17.6=11.3636}\quad\text{per event}.$$$$\boxed{Q_{\mathrm{DT}}/A_{\mathrm{DT}}=3.52,\quad Q_f/A_f=.847458\,\mathrm{MeV/nucleon}}.$$

(b) Interpretation and further calculation

$$\boxed{\frac{(E/m)_{\mathrm{DT}}}{(E/m)_f}=\frac{17.6/5}{200/236}=4.1536}.$$$$E_{\mathrm{electric}}=\eta f_{\mathrm{reacted}}m(E/m)\quad\text{before auxiliary-energy costs}.$$

Physical check

Fewer nucleons are consumed per fusion event. Real fuel utilization, recoverable fractions and conversion losses matter in an engineering comparison.