The basic source of nuclear energy lies in the equivalence of mass and energy proposed by Einstein and embodied in relation :
E=Mc2

If four hydrogen nuclei fuse together to form a helium nucleus there is a certain amount of mass converted into energy. If we write the small mass difference as ?m then:

?m=4mH -mhe

where mH denotes the mass of the hydrogen nucleus (proton) and mH denotes the mass of the helium nucleus. The mass of the nucleus is exceedingly small, and so nuclear masses are conventionally measured in atomic mass units (Amu) on a scale where the mass of the normal carbon nucleus (carbon-12) has the value 12.000. On this scale mH = 1-0081 and mHe = 4.0039. (1 Amu ^ 1.66X 10-27kg). The quoted numbers give Am = 0.0285 atomic mass units from four hydrogen nuclei. In percentage terms, when four hydrogen nuclei unite to form a helium nucleus, 0.7 per cent of the mass vanishes. Multiplication by the velocity of the light squared (c2 = 9 X 1016 m2 s-2) gives an energy release of 6 X 1014 joules per kilogram of hydrogen processed. This energy release of 2 x 108kwH per kilogram vastly exceeds that of thermal cooling or coal. Indeed if the whole Sun were to be made of hydrogen and could convert it all to helium it would produce:
(6 x 1014 x (2 x 1030)
(energy release per kg) x (mass in kilograms)
1045 joules in its lifetime. Radiation of this energy bank at the present rate (L0 ^4 x 1026 watts) gives a lifetime of 1011 years. Clearly nuclear energy production is a viable source of fuel for the Sun, since it can keep up the supply for considerably longer than the known age of the Solar System.

The mass difference mentioned above is essentially the difference m the energy that binds together the hydrogen nucleus and the helium nucleus. Figure 3.7 shows a plot of binding energy per nucleon against atomic mass number. A nucleon is a member of a nucleus that is a proton or a neutron. A hydrogen nucleus (consisting of one proton) contains one nucleon; a helium nucleus (consisting of two protons and two neutrons) contains four nucleons. Is only a rough guide and does not show fine structure .The peak of the binding energy curve occurs somewhere near atomic mass number 56, corresponding to iron (56Fe). This means that the nuclei near iron have suffered the largest loss of mass per nucleon in their formation from separate protons and neutrons, since they are the most strongly bound nuclei. The two possible ways in which energy release by nuclear transmutation can occur now become clear from further consideration of figure 3.7. First let us look at the heaviest elements, such as uranium. Relative to iron these are loosely bound (low binding energy per nucleon). So if we can break uranium into smaller fragments they will be more tightly bound, and mass would be lost, releasing energy in the process. We call this means of gaining energy NUCLEAR FISSION. It is applied in atomic power stations and atomic bombs. Another way of gaining energy is to persuade the lightest elements such as hydrogen to team up and form heavier chunks of nuclear material, such as helium, carbon, oxygen and iron, because this also increases the binding of the nuclei and releases energy. This method, termed NUCLEAR FUSION, is applied in the hydrogen bomb; scientists and engineers hope that one day they will be able to control the reaction and produce cheap energy from nuclear fusion reactors.

In stars the most important nuclear process is the fusion of hydrogen to form helium. Further fusion to carbon and to iron and beyond may also occur. This is stellar alchemy

There are two important nuclear reactions for making helium from hydrogen: one is direct – the proton-proton chain ; the other uses carbon as a catalyst and it is called the carbon-nitrogen cycle.
The PROTON-PROTON CHAIN (p-p chain) proceeds as follows :
2H + *H ->3He fy
3He + 3He >4He + AH

The reactions have been written in a nuclear physics shorthand which can easily be* unravel led with a little effort. The number to the top left of an element is its atomic mass number, which indicates the number of nucleons: for example 2H is a hydrogen nucleus or proton, 2H is heavy hydrogen, a deuteron, consisting of a proton and neutron, 3He is an isotope of helium consisting of two protons and one neutron and 4He is the usual variety of helium nucleus consisting of two protons and two neutrons. e+ denotes positive electron, or positron, which is released during the first stage of the reaction! It is an anti-matter particle and it interacts quickly with an electron; they annihilate one another producing two high-energy photons or gamma rays, v symbolizes a neutrino, which is also produced in the first reaction. It is a fundamental particle without charge or rest mass and it rarely interacts with other particles; it leaves the star at the speed of light taking away with it some of the energy of the reaction, y denotes a photon or high-energy gamma ray. The various reactions are shown schematically . The proton-proton reaction may proceed slightly differently in some circumstances going through the re¬actions

In these reactions the same notation is used for the nucleons as before and note that Li is lithium. B is boron, and Be is berylium. It is a matter of chance whether the newly produced 3He nucleus interacts with a 3Hc or a 4Hc nucleus; the chance can be calculated however. Also if 7Be, that is, berylium with seven nucleons (four protons and three neutrino), is made, it may either capture an electron and emit a neutrino to become ‘Li, or may interact with a further proton to make 8B, boron 8. In all cases the net effect has been to convert four hydrogen nuclei (protons) into a helium nucleus.

The energy released in the hydrogen-helium fusion reactions is about 4 x 10-12 joules per helium atom formed or about 1 X 10-12 joules per hydrogen atom destroyed. (This number translates directly into the quantity 6 X 1014 joules per kg discussed previously). The effective energy release in the CN cycle is slightly less than the p-p chain because the neutrinos in the CN cycle reaction are more energetic and therefore remove a larger amount of the created energy.

The CN cycle is the dominant energy-producing mechanism at hotter temperatures (exceeding about 1.6x 107K), whereas the p-p chain dominates at cooler temperatures. Neither reaction pro¬duces significant energy at temperatures below about 7 X 106K. It is important to note that all nuclear reactions are very sensitive to the exact temperature of the reacting material.

Many other nuclear reactions may occur in stars at various phases of their evolution. For example, helium may fuse to carbon through the TRIPLE-ALPHA REACTION, so called because an alpha particle is an alternative name for a helium nucleus. We may write the reaction thus:
34He->12C-f 2y

It releases 4 x 10-13 joules for each 4He nucleus destroyed. The triple-alpha reaction occurs at temperatures near 2 x 108K. There are further, more complicated reactions whereby carbon fuses to oxygen, sodium and magnesium, thence to silicon and so on up to iron. These reactions are discussed in chapter 7. Fusion reactions beyond iron are ENDOTHERMIC, that is to say they absorb energy when they take place. But they may occur in certain astrophysical situations especially in supernova explosions when a lot of neutrons are released which can build up elements in the periodic table beyond iron. The reactions after carbon contribute very little to the energy production; their main importance lies in synthesizing the chemical elements (see chapter 7). The main energy -producing reactions in stars are therefore hydrogen fusing to helium and helium fusing to carbon and oxygen.

The neutrinos produced by nuclear reactions travel directly out of the star and do not contribute to the measured photon luminosity If they could be detected on Earth they would give direct information about the physical conditions at the centres of the stars. With present detection equipment the Sun is the only star close enough possibly to give a detectable neutrino flux and a detector has been placed 1.5km underground in a gold mine to shield it from cosmic rays. The detector consists of an olympic-size swimming-pool full of perehloroethylene (C2C14). Neutrinos interact with heavy chlorine in the reaction :
V+37Cl->37Ar-e-

To produce 37Ar (argon), and the 37Ar is captured and measured. The experimental details are complicated. There may be a dis-crepancy between the observed and theoretically predicted flux of neutrinos. If so. several severe problems are posed for the usual interpretation of stellar structure: but until the experimental complexities are fully understood and the experiment has been shown to be repeatable it seems best to reserve judgement.

Now that we have outlined the nuclear reactions you should have some impression of the tremendous energy that is released deep inside the stars. We can pose the question :if the reactions are such prodigious suppliers of energy why are star Not blasted to pieces in gigantic explosions as soon as they form ?How do stars tame the nuclear fury?

The answer is that an important feature of the nuclear processes is that they are self-stabilizing in the following sense. Consider a disturbance which causes the star to contract slightly. This causes a density and temperature increase in the nuclear reaction region, which speeds up the reactions that then produce energy more quickly. However the heating associated with the extra energy causes an extra outward pressure which tends to oppose the original contraction. Similarly a slight expansion causes a fall in the rate of energy generation and in the pressure. At most phases in the evolution of a star there is a perfect balance between the rate of energy radiated from the stellar surface and the rate of energy production in the central regions. If there is not a balance (sup¬pose, for example the energy production fell behind the surface demand ),then the deficit would be made up by gravitational above ,lead to an enhancement into balance with the energy radiated at the surface

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