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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 H + 3 H 4 He + n over the reaction 2 H + 2 H 3 He + n ?

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.

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"} {}

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 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

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} {} .

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)

Tritium is naturally rare, but can be produced by the reaction n + 2 H 3 H + γ . How much energy in MeV is released in this neutron capture?

Two fusion reactions mentioned in the text are

n + 3 He 4 He + γ size 12{n +"" lSup { size 8{3} } "He" rightarrow "" lSup { size 8{4} } "He"+γ} {}

and

n + 1 H 2 H + γ size 12{n +"" lSup { size 8{1} } H rightarrow "" lSup { size 8{2} } H+γ} {} .

Both reactions release energy, but the second also creates more fuel. Confirm that the energies produced in the reactions are 20.58 and 2.22 MeV, respectively. Comment on which product nuclide is most tightly bound, 4 He size 12{"" lSup { size 8{4} } "He"} {} or 2 H size 12{"" lSup { size 8{2} } H} {} .

E = m i m f c 2 E 1 = 1.008665 + 3.016030 4.002603 ( 931.5 MeV ) = 20.58 MeV E 2 = 1 . 008665 + 1 . 007825 2 . 014102 ( 931.5 MeV ) = 2.224 MeV

4 He is more tightly bound, since this reaction gives off more energy per nucleon. size 12{"" lSup { size 8{4} } "He"} {}

(a) Calculate the number of grams of deuterium in an 80,000-L swimming pool, given deuterium is 0.0150% of natural hydrogen.

(b) Find the energy released in joules if this deuterium is fused via the reaction 2 H + 2 H 3 He + n size 12{"" lSup { size 8{2} } H+"" lSup { size 8{2} } H rightarrow "" lSup { size 8{3} } "He"+n} {} .

(c) Could the neutrons be used to create more energy?

(d) Discuss the amount of this type of energy in a swimming pool as compared to that in, say, a gallon of gasoline, also taking into consideration that water is far more abundant.

How many kilograms of water are needed to obtain the 198.8 mol of deuterium, assuming that deuterium is 0.01500% (by number) of natural hydrogen?

1 . 19 × 10 4 kg size 12{1 "." "19" times "10" rSup { size 8{4} } `"kg"} {}

The power output of the Sun is 4 × 10 26 W size 12{4 times "10" rSup { size 8{"26"} } `W} {} .

(a) If 90% of this is supplied by the proton-proton cycle, how many protons are consumed per second?

(b) How many neutrinos per second should there be per square meter at the Earth from this process? This huge number is indicative of how rarely a neutrino interacts, since large detectors observe very few per day.

Another set of reactions that result in the fusing of hydrogen into helium in the Sun and especially in hotter stars is called the carbon cycle. It is

12 C + 1 H 13 N + γ , 13 N 13 C + e + + v e , 13 C + 1 H 14 N + γ , 14 N + 1 H 15 O + γ , 15 O 15 N + e + + v e , 15 N + 1 H 12 C + 4 He.

Write down the overall effect of the carbon cycle (as was done for the 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} {} ). Note the number of protons ( 1 H ) required and assume that the positrons ( e + size 12{e rSup { size 8{+{}} } } {} ) annihilate electrons to form more γ size 12{γ} {} rays.

2 e + 4 1 H 4 He + + 2 v e

(a) Find the total energy released in MeV in each carbon cycle (elaborated in the above problem) including the annihilation energy.

(b) How does this compare with the proton-proton cycle output?

Verify that the total number of nucleons, total charge, and electron family number are conserved for each of the fusion reactions in the carbon cycle given in the above problem. (List the value of each of the conserved quantities before and after each of the reactions.)

(a) A =12+1=13 size 12{A"=12+1=13"} {} , Z =6+1=7 size 12{Z"=6+1=7"} {} , efn = 0 = 0 size 12{"efn"=0=0} {}

(b) A =13=13 size 12{A"=13=13"} {} , Z =7=6+1 size 12{Z"=7=6+1"} {} , efn = 0 = 1 + 1 size 12{"efn"=0= - 1+1} {}

(c) A =13 + 1=14 size 12{A"=13"+"1=14"} {} , Z =6+1=7 size 12{Z"=6+1=7"} {} , efn = 0 = 0 size 12{"efn"=0=0} {}

(d) A =14 + 1=15 size 12{A"=14"+"1=15"} {} , Z =7+1=8 size 12{Z"=7+1=8"} {} , efn = 0 = 0 size 12{"efn"=0=0} {}

(e) A =1 5 =15 size 12{A"=1"5"=15"} {} , Z =8=7+1 size 12{Z"=8=7+1"} {} , efn = 0 = 1 + 1 size 12{"efn"=0= - 1+1} {}

(f) A =15 + 1=12 + 4 size 12{A"=15"+"1=12"+4} {} , Z =7+1=6 + 2 size 12{Z"=7+1=6"+2} {} , efn = 0 = 0 size 12{"efn"=0=0} {}

Integrated Concepts

The laser system tested for inertial confinement can produce a 100-kJ pulse only 1.00 ns in duration. (a) What is the power output of the laser system during the brief pulse?

(b) How many photons are in the pulse, given their wavelength is 1.06 µm ?

(c) What is the total momentum of all these photons?

(d) How does the total photon momentum compare with that of a single 1.00 MeV deuterium nucleus?

Integrated Concepts

Find the amount of energy given to the 4 He size 12{"" lSup { size 8{4} } "He"} {} nucleus and to the γ size 12{γ} {} ray in the reaction n + 3 He 4 He + γ size 12{n+ rSup { size 8{3} } "He" rightarrow rSup { size 8{4} } "He"+γ} {} , using the conservation of momentum principle and taking the reactants to be initially at rest. This should confirm the contention that most of the energy goes to the γ size 12{γ} {} ray.

E γ = 20.6 MeV

E 4 He = 5.68 × 10 -2 MeV

Integrated Concepts

(a) What temperature gas would have atoms moving fast enough to bring two 3 He size 12{"" lSup { size 8{3} } "He"} {} nuclei into contact? Note that, because both are moving, the average kinetic energy only needs to be half the electric potential energy of these doubly charged nuclei when just in contact with one another.

(b) Does this high temperature imply practical difficulties for doing this in controlled fusion?

Integrated Concepts

(a) Estimate the years that the deuterium fuel in the oceans could supply the energy needs of the world. Assume world energy consumption to be ten times that of the United States which is 8 × 10 19 size 12{8 times "10" rSup { size 8{"19"} } } {} J/y and that the deuterium in the oceans could be converted to energy with an efficiency of 32%. You must estimate or look up the amount of water in the oceans and take the deuterium content to be 0.015% of natural hydrogen to find the mass of deuterium available. Note that approximate energy yield of deuterium is 3 . 37 × 10 14 size 12{3 "." "37" times "10" rSup { size 8{"14"} } } {} J/kg.

(b) Comment on how much time this is by any human measure. (It is not an unreasonable result, only an impressive one.)

(a) 3 × 10 9 y size 12{3 times "10" rSup { size 8{9} } } {}

(b) This is approximately half the lifetime of the Earth.

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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How we can toraidal magnetic field
Aditya Reply
How we can create polaidal magnetic field
Aditya
4
Mykayuh Reply
Because I'm writing a report and I would like to be really precise for the references
Gre Reply
where did you find the research and the first image (ECG and Blood pressure synchronized)? Thank you!!
Gre Reply
Practice Key Terms 6

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Source:  OpenStax, Physics 101. OpenStax CNX. Jan 07, 2013 Download for free at http://legacy.cnx.org/content/col11479/1.1
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