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# Nuclear Nuclear Fusion We can therefore envision joining small nuclei

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```									                                                      Nuclear Fusion
We can therefore envision joining small nuclei together to form larger nuclei and, in the process,
converting mass into energy. This type of reaction, in which small nuclei are joined together to
form larger ones, is called nuclear fusion. To illustrate the tremendous energies released in
fusion reactions, consider the following set of reactions, which furnishes a large fraction of the
sun's energy.
1
1H    + 11H ->    1
2
H + +10 e + 00 H

where e is a positive electron(called a positron) and v is a neutrino. The deuterium H reacts
further.
2
1   H + 11 H ->        3
2 He

and then
3
2   He + 32 He ->         4
2 He   + 211 H

To find the energy liberated in this process, we must find the mass loss. The starting mass is that
of four protons, 4*1.007276 = 4.029104 u, while the final starting mass is that of the helium 4
nucleus, namely, 4.002604 - 2m = 4.001506u. Thus the mass loss is 0.0276u. This mass has an
energy equivalent of

(0.0276u) (931 MeV/u) = 25.7 MeV

But in 1 kg of helium, there are NA /4 atoms. So the energy lost in the formation of 1 kg
of helium is

Energy = 1/4(6*1026)(25.7 MeV) = 3.86*1033 eV = 6.2*1014 J

Principle, fusion is an extremely attractive energy source. Its by-product, 4He, is not a
radioactive waste, but rather a very useful and rare element.

The difficulty in obtaining a steady fusion reaction is basically that fusion can't occur
unless the protons are within the range of the nuclear strong force, about 5*10 -15. At this range,
their coulomb repulsion is enormous. Another way of stating this is that the electical potential
energy at this distance is very large, on the order of 1MeV. This is approximately the kinetic
energy protons must be given if they are to fuse before being repelied by the coulomb force. This
energy is easily attainable by means of huge particle accelerators.

We must make use of thermal collisions between protons in an extremely hot gas.

The kinetic theory of gases tells us that the average translational kinetic energy of a
particle in a gas whose temperature is 3/2kT. Setting this equal to 1 MeV, or 1.6*10 –13J,
we have 3/2(1.38*10 -23J/k)T = 1.6*10 -13 J. Thus

T = 7.6*10 9 K
Our attempts at containment involve the fact that material at these very high temperatures
is highly ionized, consisting of separate ions and electrons in a state called a plasma. Charged
particles can be confined by strong magnetic fields, but at very high temperatures and pressure,
instabilities quickly occur and ruin the containment.

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