# 32.5 Fusion  (Page 6/13)

 Page 6 / 13

## Section summary

• Nuclear fusion is a reaction in which two nuclei are combined to form a larger nucleus. It releases energy when light nuclei are fused to form medium-mass nuclei.
• Fusion is the source of energy in stars, with the proton-proton cycle,

being the principal sequence of energy-producing reactions in our Sun.

• The overall effect of the proton-proton cycle is

where the 26.7 MeV includes the energy of the positrons emitted and annihilated.

• Attempts to utilize controlled fusion as an energy source on Earth are related to deuterium and tritium, and the reactions play important roles.
• Ignition is the condition under which controlled fusion is self-sustaining; it has not yet been achieved. Break-even, in which the fusion energy output is as great as the external energy input, has nearly been achieved.
• Magnetic confinement and inertial confinement are the two methods being developed for heating fuel to sufficiently high temperatures, at sufficient density, and for sufficiently long times to achieve ignition. The first method uses magnetic fields and the second method uses the momentum of impinging laser beams for confinement.

## Conceptual questions

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

Energy input is required to fuse medium-mass nuclei, such as iron or cobalt, into more massive nuclei. Explain why.

In considering potential fusion reactions, what is the advantage of the reaction ${}^{2}\text{H}+{}^{3}\text{H}\to {}^{4}\text{He}+n$ over the reaction ${}^{2}\text{H}+{}^{2}\text{H}\to {}^{3}\text{He}+n?$

Give reasons justifying the contention made in the text that energy from the fusion reaction ${}^{2}\text{H}+{}^{2}\text{H}\to {}^{4}\text{He}+\gamma$ is relatively difficult to capture and utilize.

## Problems&Exercises

Verify that the total number of nucleons, total charge, and electron family number are conserved for each of the fusion reactions in the proton-proton cycle in

${}^{1}\text{H}+{}^{1}\text{H}\to {}^{2}\text{H}+{e}^{+}+{v}_{\text{e}},$
${}^{1}\text{H}+{}^{2}\text{H}\to {}^{3}\text{He}+\gamma ,$

and

${}^{3}\text{He}+{}^{3}\text{He}\to {}^{4}\text{He}+{}^{1}\text{H}+{}^{1}\text{H}.$

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

(a) $A\text{=1+1=2}$ , $Z\text{=1+1=1+1}$ , $\text{efn}=0=-1+1$

(b) $A\text{=1+2=3}$ , $Z\text{=1+1=2}$ , $\text{efn=0=0}$

(c) $A\text{=3+3=4+1+1}$ , $Z\text{=2+2=2+1+1}$ , $\text{efn=0=0}$

Calculate the energy output in each of the fusion reactions in the proton-proton cycle, and verify the values given in the above summary.

Show that the total energy released in the proton-proton cycle is 26.7 MeV, considering the overall effect in ${}^{1}\text{H}+{}^{1}\text{H}\to {}^{2}\text{H}+{e}^{+}+{v}_{\text{e}}$ , ${}^{1}\text{H}+{}^{2}\text{H}\to {}^{3}\text{He}+\gamma$ , and ${}^{3}\text{He}+{}^{3}\text{He}\to {}^{4}\text{He}+{}^{1}\text{H}+{}^{1}\text{H}$ and being certain to include the annihilation energy.

$\begin{array}{lll}E& =& \left({m}_{\text{i}}-{m}_{\text{f}}\right){c}^{2}\\ & =& \left[4m\left({}^{1}\text{H}\right)-m\left({}^{4}\text{He}\right)\right]{c}^{2}\\ & =& \left[4\left(1.007825\right)-4\text{.}\text{002603}\right]\left(\text{931.5 MeV}\right)\\ & =& \text{26.73 MeV}\end{array}$

Verify by listing the number of nucleons, total charge, and electron family number before and after the cycle that these quantities are conserved in the overall proton-proton cycle in $2{e}^{-}+4{}^{1}\text{H}\to {}^{4}\text{He}+{2v}_{\text{e}}+6\gamma$ .

The energy produced by the fusion of a 1.00-kg mixture of deuterium and tritium was found in Example Calculating Energy and Power from Fusion . Approximately how many kilograms would be required to supply the annual energy use in the United States?

$3.12×{\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}\text{kg}$ (about 200 tons)

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