13.7 Nuclear Energy

The curve of binding energy per nucleon \(E_{bn}\) , given in Fig. 13.1, has a long flat middle region between A = 30 and A = 170. In this region the binding energy per nucleon is nearly constant (8.0 MeV). For the lighter nuclei region, A < 30, and for the heavier nuclei region, A > 170, the binding energy per nucleon is less than 8.0 MeV, as we have noted earlier. Now, the greater the binding energy, the less is the total mass of a bound system, such as a nucleus. Consequently, if nuclei with less total binding energy transform to nuclei with greater binding energy, there will be a net energy release. This is what happens when a heavy nucleus decays into two or more intermediate mass fragments (fission) or when light nuclei fuse into a havier nucleus (fusion.)

Exothermic chemical reactions underlie conventional energy sources such as coal or petroleum. Here the energies involved are in the range of electron volts. On the other hand, in a nuclear reaction, the energy release is of the order of MeV. Thus for the same quantity of matter, nuclear sources produce a million times more energy than a chemical source. Fission of 1 kg of uranium, for example, generates \(10^{14}\) J of energy; compare it with burning of 1 kg of coal that gives \(10^{7}\) J.

13.7.1 Fission

New possibilities emerge when we go beyond natural radioactive decays and study nuclear reactions by bombarding nuclei with other nuclear particles such as proton, neutron, α-particle, etc.

A most important neutron-induced nuclear reaction is fission. An example of fission is when a uranium isotope \({ }_{92}^{235} \mathrm{U}\) bombarded with a neutron breaks into two intermediate mass nuclear fragments \[ { }_{0}^{1} \mathrm{n}+{ }_{92}^{235} \mathrm{U} \rightarrow{ }_{92}^{236} \mathrm{U} \rightarrow{ }_{56}^{144} \mathrm{Ba}+{ }_{36}^{89} \mathrm{Kr}+3{ }_{0}^{1} \mathrm{n} \] The same reaction can produce other pairs of intermediate mass fragments \[ \begin{aligned} &{ }_{0}^{1} \mathrm{n}+{ }_{92}^{235} \mathrm{U} \rightarrow{ }_{92}^{236} \mathrm{U} \rightarrow{ }_{51}^{133} \mathrm{Sb}+{ }_{41}^{99} \mathrm{Nb}+4{ }_{0}^{1} \mathrm{n}\\ &\text { Or, as another example, }\\ &{ }_{0}^{1} \mathrm{n}+{ }_{92}^{235} \mathrm{U} \rightarrow{ }_{54}^{140} \mathrm{Xe}+{ }_{38}^{94} \mathrm{Sr}+2{ }_{0}^{1} \mathrm{n} \end{aligned} \] The fragment products are radioactive nuclei; they emit β particles in succession to achieve stable end products.

The energy released (the Q value ) in the fission reaction of nuclei like uranium is of the order of 200 MeV per fissioning nucleus. This is estimated as follows:

Let us take a nucleus with A = 240 breaking into two fragments each of A = 120. Then \[ E_{b n} \text { for } A=240 \text { nucleus is about } 7.6 \mathrm{MeV} \] \[ E_{b n} \text { for the two } A=120 \text { fragment nuclei is about } 8.5 \mathrm{MeV} \] \[ \therefore \text { Gain in binding energy for nucleon is about } 0.9 \mathrm{MeV} \text { . } \] Hence the total gain in binding energy is 240×0.9 or 216 MeV.

The disintegration energy in fission events first appears as the kinetic energy of the fragments and neutrons. Eventually it is transferred to the surrounding matter appearing as heat. The source of energy in nuclear reactors, which produce electricity, is nuclear fission. The enormous energy released in an atom bomb comes from uncontrolled nuclear fission. We discuss some details in the next section how a nuclear reactor functions.

13.7.2 Nuclear reactor

Notice one fact of great importance in the fission reactions given in Eqs. (13.26) to (13.28). There is a release of extra neutron (s) in the fission process. Averagely, 2½ neutrons are released per fission of uranium nucleus. It is a fraction since in some fission events 2 neutrons are produced, in some 3, etc. The extra neutrons in turn can initiate fission processes, producing still more neutrons, and so on. This leads to the possibility of a chain reaction, as was first suggested by Enrico Fermi. If the chain reaction is controlled suitably, we can get a steady energy output. This is what happens in a nuclear reactor. If the chain reaction is uncontrolled, it leads to explosive energy output, as in a nuclear bomb.

There is, however, a hurdle in sustaining a chain reaction, as described here. It is known experimentally that slow neutrons (thermal neutrons) are much more likely to cause fission in \({ }_{92}^{235} \mathrm{U}\) than fast neutrons. Also fast neutrons liberated in fission would escape instead of causing another fission reaction.

The average energy of a neutron produced in fission of \({ }_{92}^{235} \mathrm{U}\) is \(2 \mathrm{MeV}\) These neutrons unless slowed down will escape from the reactor without interacting with the uranium nuclei, unless a very large amount of fissionable material is used for sustaining the chain reaction. What one needs to do is to slow down the fast neutrons by elastic scattering with light nuclei. In fact, Chadwick's experiments showed that in an elastic collision with hydrogen the neutron almost comes to rest and proton carries away the energy. This is the same situation as when a marble hits head-on an identical marble at rest. Therefore, in reactors, light nuclei called moderators are provided along with the fissionable nuclei for slowing down fast neutrons. The moderators commonly used are water, heavy water \(\left(\mathrm{D}_{2} \mathrm{O}\right)\) and graphite. The Apsara reactor at the Bhabha Atomic Research Centre (BARC), Mumbai, uses water as moderator. The other Indian reactors, which are used for power production, use heavy water as moderator.

Because of the use of moderator, it is possible that the ratio, K, of number of fission produced by a given generation of neutrons to the number of fission of the preceeding generation may be greater than one. This ratio is called the multiplication factor; it is the measure of the growth rate of the neutrons in the reactor. For K = 1, the operation of the reactor is said to be critical, which is what we wish it to be for steady power operation. If K becomes greater than one, the reaction rate and the reactor power increases exponentially. Unless the factor K is brought down very close to unity, the reactor will become supercritical and can even explode. The explosion of the Chernobyl reactor in Ukraine in 1986 is a sad reminder that accidents in a nuclear reactor can be catastrophic.

The reaction rate is controlled through control-rods made out of neutron-absorbing material such as cadmium. In addition to control rods, reactors are provided with safety rods which, when required, can be inserted into the reactor and K can be reduced rapidly to less than unity.

The more abundant isotope \({ }_{92}^{238} \mathrm{U}\) in naturally occurring uranium is non-fissionable. When it captures a neutron, it produces the highly radioactive plutonium through these reactions \[ \begin{array}{c} { }_{92}^{238} \mathrm{U}+\mathrm{n} \rightarrow{ }_{92}^{239} \mathrm{U} \rightarrow{ }_{93}^{239} \mathrm{~Np}+e^{-}+\bar{v} \\ { }_{93}^{239} \mathrm{~Np} \rightarrow{ }_{94}^{239} \mathrm{Pu}+e^{-}+\bar{v} \end{array} \] Plutonium undergoes fission with slow neutrons.

Figure 13.5 shows the schematic diagram of a nuclear reactor based on thermal neutron fission. The core of the reactor is the site of nuclear fission. It contains the fuel elements in suitably fabricated form. The fuel may be say enriched uranium (i.e., one that has greater abundance of \({ }_{92}^{235}\) U than naturally occurring uranium). The core contains a moderator to slow down the neutrons. The core is surrounded by a reflector to reduce leakage. The energy (heat) released in fission is continuously removed by a suitable coolant. A containment vessel prevents the escape of radioactive fission products. The whole assembly is shielded to check harmful radiation from coming out. The reactor can be shut down by means of rods (made of, for example, cadmium) that have high absorption of neutrons. The coolant transfers heat to a working fluid which in turn may produce stream. The steam drives turbines and generates electricity.

Like any power reactor, nuclear reactors generate considerable waste products. But nuclear wastes need special care for treatment since they are radioactive and hazardous. Elaborate safety measures, both for reactor operation as well as handling and reprocessing the spent fuel, are required. These safety measures are a distinguishing feature of the Indian Atomic Energy programme. An appropriate plan is being evolved to study the possibility of converting radioactive waste into less active and short- lived material.

13.7.3 Nuclear fusion – energy generation in stars

When two light nuclei fuse to form a larger nucleus, energy is released, since the larger nucleus is more tightly bound, as seen from the binding energy curve in Fig.13.1. Some examples of such energy liberating nuclear fusion reactions are :

\[ \begin{array}{l} { }_{1}^{1} \mathrm{H}+{ }_{1}^{1} \mathrm{H} \rightarrow{ }_{1}^{2} \mathrm{H}+e^{+}+v+0.42 \mathrm{MeV} \\ { }_{1}^{2} \mathrm{H}+{ }_{1}^{2} \mathrm{H} \rightarrow{ }_{2}^{3} \mathrm{He}+n+3.27 \mathrm{MeV} \\ { }_{1}^{2} \mathrm{H}+{ }_{1}^{2} \mathrm{H} \rightarrow{ }_{1}^{3} \mathrm{H}+{ }_{1}^{1} \mathrm{H}+4.03 \mathrm{MeV} \end{array} \]

In the first reaction, two protons combine to form a deuteron and a positron with a release of 0.42 MeV energy. In reaction [13.29(b)], two deuterons combine to form the light isotope of helium. In reaction (13.29c), two deuterons combine to form a triton and a proton. For fusion to take place, the two nuclei must come close enough so that attractive short-range nuclear force is able to affect them. However, since they are both positively charged particles, they experience coulomb repulsion. They, therefore, must have enough energy to overcome this coulomb barrier. The height of the barrier depends on the charges and radii of the two interacting nuclei. It can be shown, for example, that the barrier height for two protons is ~ 400 keV, and is higher for nuclei with higher charges. We can estimate the temperature at which two protons in a proton gas would (averagely) have enough energy to overcome the coulomb barrier: \[ (3 / 2) k T=K \simeq 400 \mathrm{keV}, \text { which gives } \mathrm{T} \sim 3 \times 10^{9} \mathrm{~K} \]

When fusion is achieved by raising the temperature of the system so that particles have enough kinetic energy to overcome the coulomb repulsive behaviour, it is called thermonuclear fusion.

Thermonuclear fusion is the source of energy output in the interior of stars. The interior of the sun has a temperature of 1.5×1\(0^{7}\) K, which is considerably less than the estimated temperature required for fusion of particles of average energy. Clearly, fusion in the sun involves protons whose energies are much above the average energy.

The fusion reaction in the sun is a multi-step process in which the hydrogen is burned into helium. Thus, the fuel in the sun is the hydrogen in its core. The proton-proton (p, p) cycle by which this occurs is represented by the following sets of reactions:

\[ \begin{array}{l} { }_{1}^{1} \mathrm{H}+{ }_{1}^{1} \mathrm{H} \rightarrow{ }_{1}^{2} \mathrm{H}+e^{+}+v+0.42 \mathrm{MeV} \\ e^{+}+e^{-} \rightarrow \gamma+\gamma+1.02 \mathrm{MeV} \\ { }_{1}^{2} \mathrm{H}+{ }_{1}^{1} \mathrm{H} \rightarrow{ }_{2}^{3} \mathrm{He}+\gamma+5.49 \mathrm{MeV} \\ { }_{2}^{3} \mathrm{He}+{ }_{2}^{3} \mathrm{He} \rightarrow{ }_{2}^{4} \mathrm{He}+{ }_{1}^{1} \mathrm{H}+{ }_{1}^{1} \mathrm{H}+12.86 \mathrm{MeV} \end{array} \]

For the fourth reaction to occur, the first three reactions must occur twice, in which case two light helium nuclei unite to form ordinary helium nucleus. If we consider the combination 2(i) + 2(ii) + 2(iii) +(iv), the net effect is

\[ \begin{array}{l} 4_{1}^{1} \mathrm{H}+2 e^{-} \rightarrow{ }_{2}^{4} \mathrm{He}+2 v+6 \gamma+26.7 \mathrm{MeV} \\ \text { or }\left(4_{1}^{1} \mathrm{H}+4 e^{-}\right) \rightarrow\left({ }_{2}^{4} \mathrm{He}+2 e^{-}\right)+2 v+6 \gamma+26.7 \mathrm{MeV} \end{array} \]

Thus, four hydrogen atoms combine to form an \({ }_{2}^{4}\) He atom with a release of \(26.7 \mathrm{MeV}\) of energy.

Helium is not the only element that can be synthesized in the interior of a star. As the hydrogen in the core gets depleted and becomes helium, the core starts to cool. The star begins to collapse under its own gravity which increases the temperature of the core. If this temperature increases to about \(10^{8}\) K, fusion takes place again, this time of helium nuclei into carbon. This kind of process can generate through fusion higher and higher mass number elements. But elements more massive than those near the peak of the binding energy curve in Fig. 13.1 cannot be so produced.

The age of the sun is about \( 5 \times 10^{9} \) y and it is estimated that there is enough hydrogen in the sun to keep it going for another 5 billion years. After that, the hydrogen burning will stop and the sun will begin to cool and will start to collapse under gravity, which will raise the core temperature. The outer envelope of the sun will expand, turning it into the so called red giant.

13.7.4 Controlled thermonuclear fusion

The natural thermonuclear fusion process in a star is replicated in a thermonuclear fusion device. In controlled fusion reactors, the aim is to generate steady power by heating the nuclear fuel to a temperature in the range of \(10^{8}\) K. At these temperatures, the fuel is a mixture of positive ions and electrons (plasma). The challenge is to confine this plasma, since no container can stand such a high temperature. Several countries around the world including India are developing techniques in this connection. If successful, fusion reactors will hopefully supply almost unlimited power to humanity.