Physics Nuclear Energy, Fission And Nuclear reactor

Topic Covered

`color{blue}{star}` NUCLEAR ENERGY
`color{blue}{star}` Fission
`color{blue}{star}` Nuclear reactor


`color{blue} ✍️`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).

`color{blue} ✍️`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.

`color{blue} ✍️`This feature of the binding energy curve means that nuclei in the middle region `30 ≤ A ≤ 170` are more tightly bound than nuclei with `A < 30` and `A > 170 .` Energy then can be released if less tightly bound nuclei are transmuted into more tightly bound nuclei. Two such processes, which we have already referred to, are fission and fusion.

`color{blue} ✍️`In conventional energy sources like coal or petroleum, energy is released through chemical reactions. The energies involved are of the order of electron volts per atom.

`color{blue} ✍️`As we have seen, energies involved in nuclear processes are million times larger (in MeVs per nucleon). This means that for the same quantity of matter, nuclear sources will give a million times larger energy than conventional sources. One kilogram of coal on burning gives `10^7` J of energy, whereas 1 kg of uranium, which undergoes fission, will generate on fission `10^14` J of energy.


`color{blue} ✍️`Soon after the discovery of neutron by Chadwick, Enrico Fermi found that when neutrons bombard various elements, new radioactive elements are produced.

`color{blue} ✍️`However, when a neutron was bombared on a uranium target, the uranium nucleus broke into two nearly equal fragments releasing great amount of energy.

`color{blue} ✍️`An example of such a reaction is

`color{navy}(text()_(0)^(1)n + text()_(92)^(235)U ->text()_(92)^(236)U->text()_(56)^(144)Ba+ text()_(36)^(36)Kr +3_(0)^(1)n)`

.... (13.26)

`color{blue} ✍️`Fission does not always produce barium and krypton. A different pair can be produced, for example

`color{navy}(text()_(0)^(1)n + text()_(92)^(235)U ->text()_(92)^(235)U ->text()_(51)^(133)Sb+ text()_(41)^(99)Kr +4_(0)^(1)n)`

.... (13.27)

`color{blue} ✍️`Still another example is

`color{navy}(text()_(0)^(1)n + text()_(92)^(235)U ->text()_(54)^(140)Xe+ text()_(38)^(94)Sr +4_(0)^(1)n)`


`color{blue} ✍️`The fragment nuclei produced in fission are highly neutron-rich and unstable. They are radioactive and emit beta particles in succession until each reaches a stable end product.

`color{blue} ✍️`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:

`color{blue} ✍️`Let us take a nucleus with `A = 240` breaking into two fragments each of `A = 120`. Then `E_(bn)` for A = 240 nucleus is about 7.6 MeV,

`color{purple}(E_(bn)) \ \ "for the two A = 120 fragment nuclei is about 8.5 MeV.")`

`color{purple}(∴ "Gain in binding energy for nucleon is about 0.9 MeV.")`

`color{blue} ✍️`Hence the total gain in binding energy is `240×0.9` or `216 MeV`

`color{blue} ✍️`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.

`color{blue} ✍️`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.

Nuclear reactor

`color{blue} ✍️`When `color{purple}(text()_(92)^(235)U)` undergoes a fission after bombarded by a neutron, it also releases an extra neutron. This extra neutron is then available for initiating fission of another `color{purple}(text()_(92)^(235)U` nucleus. In fact, on an average, `2 1/2` neutrons per fission of uranium nucleus are released.

`color{blue} ✍️`The fact that more neutrons are produced in fission than are consumed raises the possibility of a chain reaction with each neutron that is produced triggering another fission. Enrico Fermi first suggested such a possibility in 1939.

`color{blue} ✍️`The chain reaction can be either uncontrolled and rapid (as in a nuclear bomb) or controlled and steady (as in a nuclear reactor). The first leads to destruction while the latter can be harnessed to generate electric power.

`color{blue} ✍️`But soon it was discovered that neutrons liberated in fission of a uranium nucleus were so energetic that they would escape instead of triggering another fission reaction. Also, it turns out that slow neutrons have a much higher intrinsic probability of inducing fission in `color{purple}(text()_(92)^(235)U)` than fast neutrons.

`color{blue} ✍️`The average energy of a neutron produced in fission of `color{blue}(text()_(92)^(235)U)` is 2 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.

`color{blue} ✍️`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.

`color{blue} ✍️`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 `(D_2O)` and graphite.

`color{blue} ✍️`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.

`color{blue} ✍️`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.

`color{blue} ✍️`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.

`color{blue} ✍️`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.

`color{blue} ✍️`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.

`color{blue} ✍️`The abundant `color{purple}(text()_(92)^(238)U)` isotope, which does not fission, on capturing a neutron leads to the formation of plutonium. The series of reactions involved is

`color{purple}(text()_(92)^(238)U +n -> text()_(93)^(239)Np +e^- +barv)`

`color{navy}(text()_(93)^(239)Np-> text()_(94)^(239)Pu +(e^-) +barv)`


`color{blue} ✍️`Plutonium is highly radioactive and can also undergo fission under bombardment by slow neutrons.

`color{blue} ✍️`The broad outlines of a typical nuclear power plant based on pressurised-water reactor are shown in Fig. 13.5.

`color{blue} ✍️`In such a reactor, water is used both as the moderator and as the heat transfer medium. In the primary-loop, water is circulated through the reactor vessel and transfers energy at high temperature and pressure (at about `600` K and `150` atm) to the steam generator, which is part of the secondary-loop.

`color{blue} ✍️`In the steam generator, evaporation provides high-pressure steam to operate the turbine that drives the electric generator.

`color{blue} ✍️`The low-pressure steam from the turbine is cooled and condensed to water and forced back into the steam generator.
The energy released in nuclear reactions is a million times larger than in chemical reactions.

`color{blue} ✍️`Therefore, the nuclear reactors need fuel a million times less in mass than used in the chemical reactors of the same power capacity. A kilogram of `text()_(92)^(235)U` on complete fission generates about `3 × 10^4 MW.`

`color{blue} ✍️`However, in nuclear reactions highly radioactive elements are continuously produced. Therefore, an unavoidable feature of reactor operation is the accumulation of radioactive waste, including both fission products and heavy transuranic elements such as plutonium and americium.

`color{blue} ✍️`Historically energy has been produced by using chemical reactions, such as burning coal, wood, gas and petroleum products. The environmental pollution produced by these is creating serious problems due to green house effect leading to global warming.

`color{blue} ✍️`The problem encountered with the nuclear power station is that the spent fuel is highly radioactive and extremely hazardous to all forms of life on earth. 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.

`color{blue} ✍️`An appropriate plan is being evolved to study the possibility of converting radioactive waste into less active and short-lived material.

`color{purple}bbul("Nuclear fusion – energy generation in stars")`
`color{blue} ✍️`The binding energy curve shown in Fig.13.1 shows that energy can be released if two light nuclei combine to form a single larger nucleus, a process called nuclear fusion. Some examples of such energy liberating reactions are

`color{navy}(text()_(1)^(1)H+text()_(1)^(1)H-> text()_(1)^(2)He +(e^+) +nu + 0.42Mev)`


`color{navy}(text()_(1)^(2)H+text()_(1)^(2)H-> text()_(2)^(3)He +n+3.27MeV)`


`color{navy}(text()_(1)^(2)H+text()_(1)^(2)H-> H +text()_(1)^(1)H+4.03MeV)`


`color{blue} ✍️`In reaction (13.29a), 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.

`color{blue} ✍️` In reaction (13.29c), two deuterons combine to form a triton and a proton. In all these reactions, we find that two positively charged particles combine to form a larger nucleus.

`color{blue} ✍️`It must be realised that such a process is hindered by the Coulomb repulsion that acts to prevent the two positively charged particles from getting close enough to be within the range of their attractive nuclear forces and thus ‘fusing’.

`color{blue} ✍️`The height of this Coulomb barrier depends on the charges and the radii of the two interacting nuclei. For example, it can be easily shown that for two protons, the barrier height is ~ 400 keV.

`color{blue} ✍️`The barrier height for more highly charged nuclei is higher. The temperature at which protons in a proton gas would have enough energy to overcome the coulomb’s barrier is given

`color{blue} ✍️`by `color{purple}((3/2)k T = K= 400 \ \"keV and is about" \ \3 × 10^9 K.)`

`color{blue} ✍️`To generate useful amount of energy, nuclear fusion must occur in bulk matter. What is needed is to raise the temperature of the material until the particles have enough energy – due to their thermal motions alone – to penetrate the coulomb barrier. This process is called thermonuclear fusion.

`color{blue} ✍️`The temperature of the core of the sun is only about `1.5×10^7` K. Therefore, even in the sun if the fusion is to take place, it must involve protons whose energies are far above the average energy.
Thus, for thermonuclear fusion to take place, extreme conditions of temperature and pressure are required, which are available only in the interiors of stars including sun. The energy generation in stars takes place via thermonuclear fusion.

`color{blue} ✍️`The fusion reaction in the sun is a multi-step process in which hydrogen is burned into helium, hydrogen being the ‘fuel’ and helium the ‘ashes’. The proton-proton (p, p) cycle by which this occurs is represented by the following sets of reactions:

`color{navy}(text()_(1)^(1)H + text()_(1)^(1)H-> text()_(1)^(2) H+e^+ nu +0.42 MeV)`


`color{navy}(e^++e^(-) -> gamma+gamma+ 1.02 MeV)`

................. (ii)

`color{navy}(text()_(1)^(2)H +text()_(1)^(1)H->text()_(2)^(3)He + gamma+5.49MeV)`


`color{navy}(text()_(2)^(3)H + text()_(2)^(3)H ->text()_(2)^(4)He+text()_(1)^(1)H+text()_(1)^(1)H+12.86MeV)`.


`color{blue} ✍️`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 or nucleus. If we consider the combination 2(i) + 2(ii) + 2(iii) +(iv), the net effect is

`color{purple}(4_(1)^(1)H + 2 (e^-) -> text()_(2)^(4)He+2v+6gamma+26.7MeV)`


`color{blue}((4_(1)^(1)H+4e^-)-> (text()_(2)^(4)He+2e^-)+(2nu+6gamma+26.7MeV)`


`color{blue} ✍️`Thus, four hydrogen atoms combine to form an `text()_2^(4)He` atom with a release of 26.7 MeV of energy.

`color{blue} ✍️`The burning of hydrogen in the sun’s core is alchemy on a grand scale in the sense that one element is turned into another. It has been going on for about `5 × 10^9 y,` and calculations show that there is enough hydrogen to keep the sun going for about the same time into the future.

`color{blue} ✍️` In about 5 billion years, however, the sun’s core, which by that time will be largely helium, will begin to cool and the sun will start to collapse under its own gravity.

`color{blue} ✍️`This will raise the core temperature and cause the outer envelope to expand, turning the sun into what is called a red giant. If the core temperature increases to `10^8` K again, energy can be produced through fusion once more – this time by burning helium to make carbon.

`color{blue} ✍️`As a star evolves further and becomes still hotter, other elements can be formed by other fusion reactions. However, elements more massive than those near the peak of the binding energy curve of Fig. 13.1 cannot be produced by further fusion.
The energy generation in stars takes place via thermonuclear fusion.

`color{brown}bbul("Controlled thermonuclear fusion")`
`color{blue} ✍️`The first thermonuclear reaction on earth occurred at Eniwetok Atoll on November 1, 1952, when USA exploded a fusion device, generating energy equivalent to 10 million tons of TNT (one ton of TNT on explosion releases `2.6 × 10^22` MeV of energy).

`color{blue} ✍️`A sustained and controllable source of fusion power is considerably more difficult to achieve. It is being pursued vigorously in many countries around the world (including India), because fusion reactor is regarded as the future power source.
Q 3149078813

Answer the following questions:
(a) Are the equations of nuclear reactions (such as those given in Section 13.7) ‘balanced’ in the sense a chemical equation (e.g.,
`2H_2 + O_2→ 2 H_2O)` is? If not, in what sense are they balanced on both sides?
b) If both the number of protons and the number of neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice-versa) in a nuclear reaction?
(c) A general impression exists that mass-energy interconversion takes place only in nuclear reaction and never in chemical reaction. This is strictly speaking, incorrect. Explain.
Class 12 Chapter 13 Example 7

(a) A chemical equation is balanced in the sense that the number of atoms of each element is the same on both sides of the equation. A chemical reaction merely alters the original combinations of atoms. In a nuclear reaction, elements may be transmuted. Thus, the number of atoms of each element is not necessarily conserved in a nuclear reaction. However, the number of protons and the number of neutrons are both separately conserved in a nuclear reaction. [Actually, even this is not strictly true in the realm of very high energies – what is strictly conserved is the total charge and total ‘baryon number’. We need not pursue this matter here.] In nuclear reactions (e.g., Eq. 13.26), the number of protons and the number of neutrons are the same on the two sides of the equation.

(b) We know that the binding energy of a nucleus gives a negative contribution to the mass of the nucleus (mass defect). Now, since proton number and neutron number are conserved in a nuclear reaction, the total rest mass of neutrons and protons is the same on either side of a reaction. But the total binding energy of nuclei on the left side need not be the same as that on the right hand side. The difference in these binding energies appears as energy released or absorbed in a nuclear reaction. Since binding energy contributes to mass, we say that the difference in the total mass of nuclei on the two sides get converted into energy or vice-versa. It is in these sense that a nuclear reaction is an example of massenergy interconversion.

(c) From the point of view of mass-energy interconversion, a chemical reaction is similar to a nuclear reaction in principle. The energy released or absorbed in a chemical reaction can be traced to the difference in chemical (not nuclear) binding energies of atoms and molecules on the two sides of a reaction. Since, strictly speaking, chemical binding energy also gives a negative contribution (mass defect) to the total mass of an atom or molecule, we can equally well say that the difference in the total mass of atoms or molecules, on the two sides of the chemical reaction gets converted into energy or vice-versa. However, the mass defects involved in a chemical reaction are almost a million times smaller than those in a nuclear reaction.This is the reason for the general impression, (which is incorrect ) that mass-energy interconversion does not take place in a chemical reaction.