# 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)

what is angular velocity
Why does earth exert only a tiny downward pull?
hello
Islam
Why is light bright?
an 8.0 capacitor is connected by to the terminals of 60Hz whoes rms voltage is 150v. a.find the capacity reactance and rms to the circuit
thanks so much. i undersooth well
what is physics
is the study of matter in relation to energy
Kintu
a submersible pump is dropped a borehole and hits the level of water at the bottom of the borehole 5 seconds later.determine the level of water in the borehole
what is power?
power P = Work done per second W/ t. It means the more power, the stronger machine
Sphere
e.g. heart Uses 2 W per beat.
Rohit
A spherica, concave shaving mirror has a radius of curvature of 32 cm .what is the magnification of a persons face. when it is 12cm to the left of the vertex of the mirror
did you solve?
Shii
1.75cm
Ridwan
my name is Abu m.konnek I am a student of a electrical engineer and I want you to help me
Abu
the magnification k = f/(f-d) with focus f = R/2 =16 cm; d =12 cm k = 16/4 =4
Sphere
what do we call velocity
Kings
A weather vane is some sort of directional arrow parallel to the ground that may rotate freely in a horizontal plane. A typical weather vane has a large cross-sectional area perpendicular to the direction the arrow is pointing, like a “One Way” street sign. The purpose of the weather vane is to indicate the direction of the wind. As wind blows pa
hi
Godfred
Godfred
If a prism is fully imersed in water then the ray of light will normally dispersed or their is any difference?
the same behavior thru the prism out or in water bud abbot
Ju
If this will experimented with a hollow(vaccum) prism in water then what will be result ?
Anurag
What was the previous far point of a patient who had laser correction that reduced the power of her eye by 7.00 D, producing a normal distant vision power of 50.0 D for her?
What is the far point of a person whose eyes have a relaxed power of 50.5 D?
Jaydie
What is the far point of a person whose eyes have a relaxed power of 50.5 D?
Jaydie
A young woman with normal distant vision has a 10.0% ability to accommodate (that is, increase) the power of her eyes. What is the closest object she can see clearly?
Jaydie
29/20 ? maybes
Ju
In what ways does physics affect the society both positively or negatively
how can I read physics...am finding it difficult to understand...pls help
try to read several books on phy don't just rely one. some authors explain better than other.
Ju
And don't forget to check out YouTube videos on the subject. Videos offer a different visual way to learn easier.
Ju
hope that helps
Ju