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25.1Nuclear fusion
Nuclear fusion is the joining of two light nuclei into a heavier one with the associated production of energy. An example of a fusion reaction is:
H12+H13âHe24+n01
In this reaction a deuterium nucleus joins with a tritium nucleus to form a nucleus of helium and a neutron. We can work out the energy released from the mass difference for the reaction:
Mass of deuterium:
2.014102 u
Mass of tritium:
3.016049 u
Mass of helium:
4.002602 u
Mass of neutron:
1.008665 u
Îm=2.014102+3.016049â(4.002602+1.008665)=0.0189Â u
Therefore:
Q=Îmc2=0.0189Ã931.5=17.6Â MeV,
which is a lot of energy!
Conditions for fusion to take place
There are three main conditions for fusion to take place.
Temperature: For fusion to occur, the reacting nuclei must join. They have to come very close to each other, within the range of the strong nuclear force, so that they attract each other (through the strong nuclear force) and join. But nuclei are positively charged so they repel each other (through the electric force). One way to get the nuclei to come close to each other is by raising the temperature at which the nuclei are kept. At high temperatures the nuclei would be moving fast enough to overcome the Coulomb repulsion and crash into each other.
Density: The second condition is that the number density of the nuclei (number of nuclei per unit volume) must be high so that there are lots of them around for fusion to occur.
Confinement time: The third condition is that the nuclei must be maintained at high temperature and density for a time long enough for many fusion reactions to take place.
The problem is that the temperatures required are in the millions of degrees. At these temperatures matter is in the plasma state, i.e. the electrons have left the atoms, and the problem is that it is not easy to confine this very hot plasma at high density for sufficiently long times.
Whereas we face serious problems in our attempts to extract energy from nuclei through fusion, stars perfectly satisfy all criteria for nuclear fusion. Nuclear fusion provides the energy that is radiated by stars into space, the pressure to keep a star from collapsing under its own weight and the nuclear fusion reactions and related processes that are responsible for nucleosynthesis, the creation of the chemical elements. Therefore, the natural place to study fusion is the stars so we begin in SectionÂ 25.2 by discussing basic stellar properties.
CHECK YOURSELF 1
Why are high temperatures required for fusion to occur?
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WORKED EXAMPLE 25.1
Consider the fusion reaction:
H12+H12âHe23+n01
Mass of deuterium:
2.014102 u
Mass of helium:
3.016029 u
Mass of neutron:
1.008665 u
Calculate the energy released.
Answer
Îm=2Ã2.014102â(3.016029+1.008665)Â u
Îm=0.00351Â u
Therefore:
Q=Îmc2=0.00351Ã931.5=3.27Â MeV
WORKED EXAMPLE 25.2
The two deuterium nuclei in worked example 25.1 will fuse when their distance apart is of order 10â15 m. The electrostatic potential energy at this separation is of order 10â13 J. To overcome the electrostatic repulsion, a kinetic energy of this order of magnitude is required. The deuterium nuclei are kept at a temperature T. Estimate T.
Answer
Using E=32kT, we find
32kTÃ2=10â13âT=10â133Ã1.38Ã10â23â2Ã109Â K
In stars, deuterium fusion reactions take place at temperatures of order 5 Ã 108 K, which shows that at this lower temperature, some deuterium nuclei have energies that are way above the average.
TEST YOUR UNDERSTANDING
1State and explain the conditions necessary for nuclear fusion to occur.
2Calculate the energy released in the fusion reaction:
H11+H12âHe23+Î³
(Atomic masses: H11=1.007825Â u; H12=2.014102Â u; He23=3.016029Â u.)
3Deuteriumâtritium fusion, H12+H13âHe24+n01, happens at a lower temperature than deuteriumâdeuterium fusion, H12+H12âHe23+n01. Can you suggest a reason for this observation?
4State and explain one difficulty that still prevents the commercial production of energy through nuclear fusion.
5Suggest two advantages of energy production that nuclear fusion would have over energy production by nuclear fission.
