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Conceptual questions

Explain the difference between nuclear fission and nuclear fusion.

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

The nuclei produced in the fusion process have a larger binding energy per nucleon than the nuclei that are fused. That is, nuclear fusion decreases average energy of the nucleons in the system. The energy difference is carried away as radiation.

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Problems

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 H + 1 H 2 H + e + + v e ,

(ii) 1 H + 2 H 3 H e + γ , and (iii) 3 H e + 3 H e 4 H e + 1 H + 1 H .

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

i. 1 1 H + 1 1 H 1 2 H + e + + v e A i = 1 + 1 = 2 ; A f = 2 Z i = 1 + 1 = 2 Z f = 1 + 1 = 2 ;
ii. 1 1 H + 1 2 H 2 3 H + γ A i = 1 + 2 = 3 ; A f = 3 + 0 = 3 Z i = 1 + 1 = 2 Z E = 1 + 1 = 2 ;
iii. 2 3 H + 2 3 H 2 4 H + 1 1 H + 1 1 H A i = 3 + 3 = 6 ; A f = 4 + 1 + 1 = 6 Z i = 2 + 2 = 4 Z f = 2 + 1 + 1 = 4

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Calculate the energy output in each of the fusion reactions in the proton-proton chain, and verify the values determined in the preceding problem.

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

26.73 MeV

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Two fusion reactions mentioned in the text are n + 3 H e 4 H e + γ and n + 1 H 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 H e or 2 H .

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The power output of the Sun is 4 × 10 26 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. 3 × 10 38 protons/s ; b. 6 × 10 14 neutrinos/m 2 · s ;
This huge number is indicative of how rarely a neutrino interacts, since large detectors observe very few per day.

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Another set of reactions that fuses hydrogen into helium in the Sun and especially in hotter stars is called the CNO cycle:

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 H e

This process is a “cycle” because 12 C appears at the beginning and end of these reactions. Write down the overall effect of this cycle (as done for the proton-proton chain in 2 e + 4 1 H 4 H e + 2 v e + 6 γ ). Assume that the positrons annihilate electrons to form more γ rays.

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(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?

a. The atomic mass of deuterium ( 2 H ) is 2.014102 u, while that of tritium ( 3 H ) is 3.016049 u, for a total of 5.032151 u per reaction. So a mole of reactants has a mass of 5.03 g, and in 1.00 kg, there are ( 1000 g ) / ( 5.03 g / mol ) = 198.8 mol of reactants. The number of reactions that take place is therefore
( 198.8 mol ) ( 6.02 × 10 23 mol −1 ) = 1.20 × 10 26 reactions .
The total energy output is the number of reactions times the energy per reaction:
E = 3.37 × 10 14 J;
b. Power is energy per unit time. One year has 3.16 × 10 7 s , so
P = 10.7 MW .
We expect nuclear processes to yield large amounts of energy, and this is certainly the case here. The energy output of 3.37 × 10 14 J from fusing 1.00 kg of deuterium and tritium is equivalent to 2.6 million gallons of gasoline and about eight times the energy output of the bomb that destroyed Hiroshima. Yet the average backyard swimming pool has about 6 kg of deuterium in it, so that fuel is plentiful if it can be utilized in a controlled manner.

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Questions & Answers

can someone explain normalization condition
Priyojit Reply
1 millimeter is How many metres
Darling Reply
1millimeter =0.001metre
Gitanjali
The photoelectric effect is the emission of electrons when light shines on a material. 
Chris Reply
What is photoelectric effect
Amit Reply
it gives practical evidence of particke nature of light.
Omsai
particle nature
Omsai
photoelectric effect is the phenomenon of emission of electrons from a material(i.e Metal) when it is exposed to sunlight. Emitted electrons are called as photo electrons.
Anil
what are the applications of quantum mechanics to medicine?
Neptune
application of quantum mechanics in medicine: 1) improved disease screening and treatment ; using a relatively new method known as BIO- BARCODE ASSAY we can detect disease-specific clues in our blood using gold nanoparticles. 2) in Genomic medicine 3) in protein folding 4) in radio theraphy(MRI)
Anil
Quantam physics ki basic concepts?
Laxmikanta Reply
why does not electron exits in nucleaus
Kabbo Reply
electrons have negative
YASH
Proton and meltdown has greater mass than electron. So it naturally electron will move around nucleus such as gases surrounded earth
Amalesh
.......proton and neutron....
Amalesh
excuse me yash what negative
Rika
coz, electron contained minus ion
Manish
negative sign rika shrestha ji
YASH
electron is the smallest negetive charge...An anaion i.e., negetive ion contains extra electrons. How ever an atom is neutral so it must contains proton and electron
Amalesh
yes yash ji
Rika
yes friends
Prema
koantam theory
Laxmikanta
yes prema
Rika
quantum theory tells us that both light and matter consists of tiny particles which have wave like propertise associated with them.
Prema
proton and nutron nuclear power is best than proton and electron kulamb force
Laxmikanta
what is de-broglie wave length?
Ramsuphal
plot a graph of MP against tan ( Angle/2) and determine the slope of the graph and find the error in it.
Ime Reply
expression for photon as wave
BARISUA Reply
Are beta particle and eletron are same?
Amalesh Reply
yes
mari
how can you confirm?
Amalesh
sry
Saiaung
If they are same then why they named differently?
Amalesh
because beta particles give the information that the electron is ejected from the nucleus with very high energy
Absar
what is meant by Z in nuclear physic
Shubhu Reply
atomic n.o
Gyanendra
no of atoms present in nucleus
Sanjana
miss sanjana your question is wrong...question should be no of nucleus present in an atom...and answer is 1...
Owais
Owaise is right
Gitanjali
Z = number of protons in a nucleus of an atom
Shashikanth
Note on spherical mirrors
Shamanth Reply
what is Draic equation? with explanation
M.D Reply
what is CHEMISTRY
trpathy Reply
it's a subject
Akhter
it's a branch in science which deals with the properties,uses and composition of matter
Eniabire
what is a Higgs Boson please?
FRANKLINE Reply
god particles is know as higgs boson, when two proton are reacted than a particles came out which is used to make a bond between than materials
M.D
bro little abit getting confuse if i am wrong than please clarify me
M.D
the law of refraction of direct current lines at the boundary between two conducting media of
BATTULA Reply
Practice Key Terms 4

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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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