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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,
    1 H + 1 H 2 H + e + + v e       (0.42 MeV)
    1 H + 2 H 3 He + γ          (5.49 MeV)
    3 He + 3 He 4 He + 1 H + 1 H            (12.86 MeV)

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

  • The overall effect of the proton-proton cycle is
    2 e + 4 1 H 4 He + 2 v e +             (26.7 MeV),

    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?

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

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In considering potential fusion reactions, what is the advantage of the reaction 2 H + 3 H 4 He + n over the reaction 2 H + 2 H 3 He + n ?

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Give reasons justifying the contention made in the text that energy from the fusion reaction 2 H + 2 H 4 He + γ is relatively difficult to capture and utilize.

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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 H + 1 H 2 H + e + + v e , size 12{"" lSup { size 8{1} } "H "+"" lSup { size 8{1} } "H " rightarrow "" lSup { size 8{2} } H+e rSup { size 8{+{}} } +v rSub { size 8{e} } } {}
1 H + 2 H 3 He + γ ,

and

3 He + 3 He 4 He + 1 H + 1 H size 12{"" lSup { size 8{3} } "He "+"" lSup { size 8{3} } "He" rightarrow "" lSup { size 8{4} } "He"+"" lSup { size 8{1} } H+"" lSup { size 8{1} } H} {} .

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

(a) A =1+1=2 size 12{A"=1+1=2"} {} , Z =1+1=1+1 size 12{Z"=1+1=1+1"} {} , efn = 0 = 1 + 1 size 12{"efn"=0= - 1+1} {}

(b) A =1+2=3 size 12{A"=1+2=3"} {} , Z =1+1=2 size 12{Z"=1+1=2"} {} , efn=0=0 size 12{"efn=0=0"} {}

(c) A =3+3=4+1+1 size 12{A"=3+3=4+1+1"} {} , Z =2+2=2+1+1 size 12{Z"=2+2=2+1+1"} {} , efn=0=0 size 12{"efn=0=0"} {}

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

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Show that the total energy released in the proton-proton cycle is 26.7 MeV, considering the overall effect in 1 H + 1 H 2 H + e + + v e , 1 H + 2 H 3 He + γ , and 3 He + 3 He 4 He + 1 H + 1 H and being certain to include the annihilation energy.

E = m i m f c 2 = 4 m 1 H m 4 He c 2 = 4 ( 1.007825 ) 4 . 002603 ( 931.5 MeV ) = 26.73 MeV

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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 H 4 He + 2 v e + size 12{2e rSup { size 8{ - {}} } +4"" lSup { size 8{1} } H rightarrow "" lSup { size 8{4} } "He"+2v rSub { size 8{e} } +6γ} {} .

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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 × 10 5 kg size 12{2 times "10" rSup { size 8{5} } `"kg"} {} (about 200 tons)

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Questions & Answers

how can I read physics...am finding it difficult to understand...pls help
rerry Reply
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
I have a exam on 12 february
David Reply
what is velocity
Jiti
the speed of something in a given direction.
Ju
what is a magnitude in physics
Jiti Reply
Propose a force standard different from the example of a stretched spring discussed in the text. Your standard must be capable of producing the same force repeatedly.
Giovani Reply
What is meant by dielectric charge?
It's Reply
what happens to the size of charge if the dielectric is changed?
Brhanu Reply
omega= omega not +alpha t derivation
Provakar Reply
u have to derivate it respected to time ...and as w is the angular velocity uu will relace it with "thita × time""
Abrar
do to be peaceful with any body
Brhanu Reply
the angle subtended at the center of sphere of radius r in steradian is equal to 4 pi how?
Saeed Reply
if for diatonic gas Cv =5R/2 then gamma is equal to 7/5 how?
Saeed
define variable velocity
Ali Reply
displacement in easy way.
Mubashir Reply
binding energy per nucleon
Poonam Reply
why God created humanity
Manuel Reply
Because HE needs someone to dominate the earth (Gen. 1:26)
Olorunfemi
why god made humenity
Ali
and he to multiply
Owofemi
stuff happens
Ju
God plays dice
Ju
Is the object in a conductor or an insulator? Justify your answer. whats the answer to this question? pls need help figure is given above
Jun Reply
ok we can say body is electrically neutral ...conductor this quality is given to most metalls who have free electron in orbital d ...but human doesn't have ...so we re made from insulator or dielectric material ... furthermore, the menirals in our body like k, Fe , cu , zn
Abrar
when we face electric shock these elements work as a conductor that's why we got this shock
Abrar
how do i calculate the pressure on the base of a deposit if the deposit is moving with a linear aceleration
ximena Reply
Practice Key Terms 6

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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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