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Consider the fusion in helium plasma. Fi...

Consider the fusion in helium plasma. Find the temperature at which the average thermal energy 1.5 kT equals the Coulomb potential energy at 2 fm.

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Scientists are working hard to develop nuclear fusion reactor Nuclei of heavy hydrogen, _(1)^(2)H , known as deuteron and denoted by D , can be thought of as a candidate for fusion rector . The D-D reaction is _(1)^(2) H + _(1)^(2) H rarr _(2)^(1) He + n+ energy. In the core of fusion reactor, a gas of heavy hydrogen of _(1)^(2) H is fully ionized into deuteron nuclei and electrons. This collection of _1^2H nuclei and electrons is known as plasma . The nuclei move randomly in the reactor core and occasionally come close enough for nuclear fusion to take place. Usually , the temperature in the reactor core are too high and no material will can be used to confine the to plasma for a time t_(0) before the particles fly away from the core. If n is the density (number volume ) of deuterons , the product nt_(0) is called Lawson number. In one of the criteria , a reactor is termed successful if Lawson number is greater then 5 xx 10^(14) s//cm^(2) it may be helpfull to use the following boltzmann constant lambda = 8.6 xx 10^(-5)eV//k, (e^(2))/(4 pi s_(0)) = 1.44 xx 10^(-9) eVm Assume that two deuteron nuclei in the core of fusion reactor at temperature energy T are moving toward each other, each with kinectic energy 1.5 kT , when the seperation between them is large enough to neglect coulomb potential energy . Also neglate any interaction from other particle in the core . The minimum temperature T required for them to reach a separation of 4 xx 10^(-15) m is in the range

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HC VERMA-THE NUCLEOUS-Exercises
  1. Natural water contains a small amount of tritium (1^3H). This isotope ...

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  2. The count rate of nuclear radiation coming from a radioactive sample c...

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  3. The half-life of K-40 is 1.30×10^ 9 year. A sample of 1.0 g of pure ...

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  4. 80^197Hg decay to 79^197Au through electron capture with a decay const...

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  5. A radioactive isotope is being produced at a constant rate dN//dt=R in...

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  6. Consider the situation of the previous problem.suppose the production ...

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  7. In an agriculture experiment, a solution containing 1 mole of a radioa...

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  8. A vessel of vloume 125 cm^3 contains tritium (^3H,t(1//2)=12.3 y) at 5...

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  9. 83^212Bi can disintegrate either by emitting an alpha -particle or by ...

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  10. A sample contains a mixture of ^110Ag and ^108Ag isotopes each having ...

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  11. A human body excretes (removes by waste discharge, sweating, etc,) cer...

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  12. A charged capacitor of capacitance C is discharged through a resistanc...

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  13. Radioactive isotopes are produced in a nuclear physics experiment at a...

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  14. Calculate the energy released by 1 g of natural uranium assuming 200 M...

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  15. A uranium rector develops thermal energy at a rate of 300 MW. Calculat...

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  16. A town has a population of 1 million. The average electric power neede...

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  17. Calculate the Q-values of the following fusion reactions: (a)1^2H+1^2H...

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  18. Consider the fusion in helium plasma. Find the temperature at which th...

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  19. Calculate the Q-values of the fusion reaction ^4(He)+^4He=^8(Be). I...

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  20. Calculate the energy that can be obtained from 1 kg of water through t...

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