10.6 Nuclear Fusion

Where does the energy from the Sun originate?

Why does the fusion of light nuclei into heavier nuclei release energy?

Verify that the total number of nucleons, and total charge are conserved for each of the following fusion reactions in the proton-proton chain.

(i) $^{1} \text{H} + ^{1} \text{H} \rightarrow ^{2} \text{H} + e^{+} + v_{\text{e}}$,

(ii) $^{1} \text{H} + ^{2} \text{H} \rightarrow ^{3} \text{H} \text{e} + \gamma$, and (iii) $^{3} \text{H} \text{e} + ^{3} \text{H} \text{e} \rightarrow ^{4} \text{H} \text{e} + ^{1} \text{H} + ^{1} \text{H}$.

(List the value of each of the conserved quantities before and after each of the reactions.)

Show that the total energy released in the proton-proton chain is 26.7 MeV, considering the overall effect in $^{1} \text{H} + ^{1} \text{H} \rightarrow ^{2} \text{H} + e^{+} + v_{\text{e}}$, $^{1} \text{H} + ^{2} \text{H} \rightarrow ^{3} \text{H} \text{e} + \gamma$, and $^{3} \text{H} \text{e} + ^{3} \text{H} \text{e} \rightarrow ^{4} \text{H} \text{e} + ^{1} \text{H} + ^{1} \text{H}$. Be sure to include the annihilation energy.

The power output of the Sun is $4 \times 10^{26} \text{W} .$ (a) If $90 \%$ of this energy is supplied by the proton-proton chain, how many protons are consumed per second? (b) How many neutrinos per second should there be per square meter at the surface of Earth from this process?

(a) Calculate the energy released by the fusion of a 1.00-kg mixture of deuterium and tritium, which produces helium. There are equal numbers of deuterium and tritium nuclei in the mixture.

(b) If this process takes place continuously over a period of a year, what is the average power output?