Nuclear composition
An atom consists of an extremely small, positively charged nucleus surrounded by a cloud of negatively charged electrons. Although typically the nucleus is less than one ten-thousandth the size of the atom, the nucleus contains more that 99.9% of the mass of the atom. Nuclei consist of positively charged protons and electrically neutral neutrons held together by the so-called strong or nuclear force. This force is much stronger than the familiar electrostatic force that binds the electrons to the nucleus, but its range is limited to distances on the order of a few x10-15 meters. The number of protons in the nucleus, Z, is
called the atomic number. This determines what chemical element the atom is. N denotes the number of neutrons in the nucleus. The mass number A is approximately the total number of nucleons, a collective name for protons and neutrons. Therefore
A = N + Z
A given element can have many different isotopes, which differ from one another by the number of neutrons contained in the nuclei i.e. with same Z but different A (= N+Z) e.g.
1H, 2H and 3H. In a neutral atom, the number of electrons orbiting the nucleus equals the
number of protons in the nucleus. Since the electric charges of the proton and the electron are +1 and-1 respectively (in units of the proton charge), the net charge of the atom is zero. At present, there are 112 known elements, which range from the lightest, hydrogen, to the recently discovered and yet to-be-named element 112. All of the elements heavier than uranium are man made. Among the elements are approximately 270 stable isotopes, and more than 2000 unstable isotopes.
Binding energy
The binding energy (BE) of a nuclide is the energy released when the atom is synthesized from the appropriate numbers of hydrogen atoms and neutrons. The binding energies of hydrogen atoms and neutrons are thus zero in this definition. The concept of BE applies to both stable and radioactive nuclides, and the definition given above can be represented by a hypothetical equation:
Z mH + N mn = mE + BE ⇒ BE = Z mH + N mn - mE.
where mH, mn, and mE are masses of H, n, and the nuclide AEZ respectively.
The binding energy is thus the minimum energy required in order to decompose nuclide AEZ into Z H and N n, i.e., AEZ + BE = Z H + N n. The more the binding energy, the more stable is the nuclide.
The binding energies of 4He (mass 4.0260) is:
BE (3He) =(2x1.007825 + 1.008665 - 3.01603)931.481 MeV = 7.72 MeV
BE(4He) =(2x1.007825 + 2x1.008665 - 4.0026)931.481MeV = 28.30MeV.
(Here 1a.m.u. = 1.66054X10-27Kg ⇒ 931.5MeV)
The estimates here show that formation of 4He releases much more energy than the
amount of energy released when one nucleon is added to a nuclide. The binding energy of a nucleon (BEn, or BEp) is the energy released when a nucleon is added to a nuclide. The
binding energies of proton and neutron for 234U are calculated below 234U + n →235U + BE
n.
⇒ BEn = (234.040946 + 1.008665 - 235.043924) x 931.5 MeV = 5.30 MeV
The Average Binding Energy of BE per nucleon
The average binding energy, BEav, of a nuclide is its binding energy (BE) divided by the
number of nucleon in it (or mass number A), BEav, = BE/A. The average binding energy is
also called the packing fraction. This term is given to reflect the tighter the nucleons pack in a nuclide, the more energy is released.
Comparison of BE provides an indication about relative stability for similar nuclides, but BEs of different nuclides are not based on the same numbers of H atoms and neutrons. As we evaluate the average binding energy BEav of some of the nuclides, pay attention to the
variation of binding energy as A increases:
BEav (3He2) = 2.57 MeV / nucleon; BEav (4He2) = 7.08 MeV / nucleon
BEav (16O8) = 7.98 MeV / nucleon; BEav (56Fe26) = 8.79 MeV / nucleon
BEav (54Fe26) = 8.74 MeV / nucleon; BEav (208Pb82) = 7.87 MeV / nucleon
BEav (238U92) = 7.57 MeV / nucleon
In general, the binding energy BE increases as A increases. A general trend of the variation of average binding energy as a function of the mass number is sketched here. As the atomic number increases, the average binding energy increases, reaching a peak (8.79 MeV) at Fe, and then it decreases gradually to 7.6MeV for higher mass number. From the average binding energy point of view, nuclides with mass number around 58 are the most stable. This fact suggests that a large amount of energy will be liberated if heavier nuclei can somehow be split into
lighter ones or if light nuclei can somehow be joined to form heavier ones. Combining light nuclides to form heavy ones is called nuclear fusion and it usually is accompanied by a release of (fusion) energy. When a heavy nuclide split up, it is called nuclear fission.
Since the average binding energy for Fe is the highest, synthesis of Fe from hydrogen atoms and neutrons will release the most energy per nucleon compared to all other nuclides. Thus, energy will be released when light nuclides such as H and D combines to form He. The BEav is an indicator of energy frozen per nucleon in a nuclide. The more
average energy is released when a nuclide is synthesized, the less energy is frozen per nucleon in a nuclide. Thus, BEav is a parameter for the stability of a nuclide, stable and
Nuclear Size
We know that nuclei are very small. An empirical formula for the size of the nuclei, which can be measured using the form factor in elastic electron-nuclei scattering, is (A∝R3⇒R∝A1/3)
R = r0A1/3 where r0 = 1.2 fm.
This is a good approximation practically for all nuclei with A ≥ 12. Here, fm = 10−15 m, or
called “Fermi” rather than femto-meter, and the nuclei are smaller by five orders of magnitude than the atoms. What the formula means is that the nuclear density is more-or-less constant for any nuclei, ρ = 1.72 × 1038 nucleons/cm3 = 0.172 nucleons/fm3.
FISSION
Nuclear fission is a process, by which a heavy nuclide splits into two or more pieces and a great deal of energy is released or absorbed. Fission has been used for nuclear reactors and atomic bombs. The most suitable naturally occurring fuel is uranium. It occurs primarily in two forms, 235
92U (0.7%) and 23892U (99.3%). For uranium ore, the natural rate of fission is
completely negligible, but U may be made to fission by neutron capture, and as each fission results in neutron-rich daughter nuclei which release a couple of neutrons that may in turn be captured, the possibility of a typical fission reaction is.
Reaction 235
92U + n →23692U* →14156Ba + 9236Kr + 3n + Q.
Check Q = (235.043924 - 89.904703 - 141.907719 - 3 x 1.008665)(931.4812 MeV/ 1 amu)
= 191.4 MeV per fission
Thus 200 MeV, energy is released in one fission.
Number of atoms in 1 Kg of uranium = 6.023X1026 / 235
Energy produced by 1 Kg of uranium = 6.023X1026 / 235 X 200 = 5.128X1026MeV
= 5.128X1026 X 1.6X10-13 J
= 5.128X1026 X 1.6X10-13 / (3.6X106) KWh
= 2.26X107 kWh
Due to this reason, nuclear energy is being used for the generation of electricity. Application:
1. Nuclear Power generation: Produce electricity.
2. Medicine: Nuclear processes are used to provide images inside the human body, to detect and measure biochemical processes, and to provide therapy. X-Ray, MRI (Magnetic resonance imaging), Radiation Therapy etc.
3. Nuclear Weapon:
4. Research: provide a source for neutron and positron radiation, isotopes, radioactive materials etc.
Chain Reaction: A chain reaction is a self – propagating process in which number of neutrons goes on multiplying rapidly almost in geometrical progression during fission till whole of fissile material is disintegrated.
Multiplication factor (k): The ratio of secondary neutrons produced to the original neutrons is called the multiplication factor. It is defined as
No. of neutrons in any one generation K =
---No. of neutrons in the preceding generation
The fission chain reaction will be critical or steady when k = 1, it will be supercritical or building up when k < 1 and it will be dying down when k < 1.
Type of Nuclear Reactors:
Light Water and enriched Uranium: Most reactor use light water as moderator and coolant. Light water is an efficient moderator, but the proton nucleus in water tends to capture neutrons to form deuterons. Therefore light water reactors can’t use natural Ur as fuel. They use enriched Ur in which 92U235 content is about 3%.
Boiling Water Reactor: This allows steam to form and this is separated out and sent to a turbine.
Heavy Water Reactor: It is a better moderator then light water and natural Ur can be used as a fuel. It is less likely to capture neutrons.
Breeder Reactor: If 238
92U and 23290Th are incorporate in a reactor it absorb neutron such that
they are not taking part directly fission event, more new fissionable material can be produced than in consumed. This is possible in the breeder reactor.
238
92U + n →23992U + γ 239
92U →23993Np + e-(β)
239
93Np →23994Pu + e-(β)
Similarly thorium may become fissionable isotope for 233 92U 232
90Th + n →23390Th 233
90Th →23391Pa + e- (β)
233
91Pa →23392U + e-(β)
Fast neutrons are most effective in the breeder reactor. People use liquid sodium as coolant as this is more effective for heat transfer.
Parts of a Nuclear Reactor - Pressurized Water Reactor (PWR):
Nuclear reactor, device for producing controlled release of nuclear energy. Reactors can be used for research or for power production. A research reactor is designed to produce various beams of radiation for experimental application; the heat produced is a waste product and is dissipated as efficiently as possible. In a power reactor the heat produced is of primary importance for use in driving conventional heat engines; shielding controls the beams of radiation.
A typical nuclear reactor consist of five main parts 1. The fissionable material called fuel :Ur235, Th232, Pu239
2. Moderator (slows high moving neutrons) :(D2O), graphite, berllium etc.
3. Neutron reflector (check leakage of n) : Materials have low atomic weight and low absorbing cross section
4. Cooling system (absorption of heat) :Water, CO2, air
5. The safety and control system :Control chain reaction, rods of (Boron/cadmium) have large absorbing cross- section. For safety surround the system by concrete walls.
The commonly used fissionable materials are the uranium isotopes U233 and U235, the thorium isotope
Th232 and the plutonium Pu 239, Pu240
and Pu241. -Inside each fuel rod are
hundreds of pellets of uranium fuel stacked end to end.
Another component of the reactor is the moderator. The moderator slows
down the high-speed neutrons "flying" all around the reactor core. If a neutron is moving too fast, and thus is at a high-energy state, it passes right through the 235U nucleus. It must
be slowed down to be captured by the nucleus and to induce fission. The most common moderator is heavy water (D2O), graphite, beryllium etc.
By the use of reflector on the surface of reactors, leakage of neutrons can be very much reduced and the neutron flux in the interior can be increased. Materials of high scattering cross – section and low absorption cross – section are good reflectors.
The job of the coolant is to absorb the heat from the reaction. The most common coolant used in nuclear power plants today is water. In actuality, in many reactor designs the coolant and the moderator are one and the same. The coolant water is heated by the nuclear reactions going on inside the core. However, this heated water does not boil because it is kept at an extremely intense pressure, thus raising its boiling point above the normal 100° Celsius.
Also in the core are control rods. These rods have pellets inside that are made of very efficient neutron capturers. An example of such a material is cadmium or graphite. These control rods are connected to machines that can raise or lower them in the core. When they are fully lowered into the core, fission cannot occur because they absorb free neutrons. However, when they are pulled out of the reactor, fission can start again anytime a stray neutron strikes a 235U atom, thus releasing more neutrons, and starting a chain reaction.
From Fission to Electricity: A nuclear power plant produces electricity in almost exactly the same way that a conventional (fossil fuel) power plant does. A conventional power plant burns fuel to create heat. The fuel is generally coal, but oil is also sometimes used. The heat is used to raise the temperature of water, thus causing it to boil. The high temperature and intense pressure steam that results from the boiling of the water turns a turbine, which then generates electricity. A nuclear power plant works the same way, except that the heat used to boil the water is produced by a nuclear fission reaction using 235U as fuel, not the combustion of fossil fuels. A nuclear power plant uses much less fuel than a comparable fossil fuel plant. A rough estimate is that it takes 17,000 kilograms of coal to produce the same amount of electricity as 1 kilogram of nuclear uranium fuel.
FUSION
Fusion is a process, in which two or more light nuclei are meshed into larger nuclei. It is almost the exact opposite of fission. So far, fusion has only been implemented in the hydrogen bomb. However, since fusion provides a much greater supply of energy than does fission, scientists are working very hard to create fusion reactors.
The energy released from nuclear fusion reactions is at the expense of the mass. The mass differences before and after the fusion reactions are converted to energy. Thus, the energy of fusion Q can be treated as part of the reaction equation. For example, the equation of D-T fusion is,
D + T →4He + n + Q
⇒ Q = 13.136 + 14.950 - 2.425 - 8.071 = 17.6 MeV = 1.7x1012 J
The actual masses rather than mass excesses can also be used, and the calculation is just as easy. The four commonly studied fusion reactions and their Q values are:
D + T →4He + n + 17.6 MeV
D + 3He →4He + p + 18.4 MeV
D + D →3He + n + 3.3 MeV
D + D →3T + p + 4.0 MeV
Reactions D + T and D + 3He releases similar amounts
of energy, but the D + T reaction takes place at much lower temperatures and is particularly interesting from an engineering point of view.
Energy sources from fossil fuel are limited. Fission nuclear reactors have been supplying energy for decades but the problems of radioactive waste disposal have become apparent in the 1970s. In the 1980s, public faith on fission reactors has been further eroded by reactor accidents. These problems remain unsolved, and the future of fission reactors seems uncertain.
The Fusion Process
Collision
Fusion offers an important potential source of energy on earth, since it could provide enormous amounts of energy from an almost inexhaustible energy source, and produce negligible pollution. For fusion reactions to take place, D and T mixtures have to be heated to 106 degrees. At these temperatures, the mixture is plasma, no longer a gas.
In the formation of 1 gm of He 7X106 KWH of energy is released. A self-sustained fusion
reaction occurs in the hydrogen bomb. The explosive substance is a mixture of 1D2 and 1T3. To start thermonuclear reaction, it requires a very high temperature, which is obtained by exploding fission bomb first.
Fission and Fusion Yields
Radiation hazards
Most of the disadvantages with nuclear energy has to do with the inherent properties of nuclear fission. The energy and byproducts released by nuclear fission are health hazards--either because of being extremely hot, due to the highly energetic release of heat during nuclear fission, or because of the destructive effects of radiation poisoning.
Other disadvantages tend to be industrial in nature. Not only does nuclear power come with an extremely high initial expense, but the storage of waste products remains a difficult and controversial problem.
Protection: Thousands of people work with radiation and radioactive materials every day. Radiation can be handled safely, given the right tools and training. Be aware of the effects of time, distance and shielding against radiation. Exposure must be carefully monitored.
Training : When working with radiation, knowledge is the best ally. Learn the basic types of radiation, where it comes from and how to measure it. In addition, you'll need to learn how to operate scientific equipment.
1. Shielding: Radiation is blocked by shielding materials such as lead, concrete and water. Different kinds of radiation call for different types of shielding.
2. Distance: Radiation from small sources diminishes with distance. It's an inverse-square relationship so if you double the distance, the received radiation is 1/4. 3. Time: Radiation dosage is reckoned against time. Safe practices allow brief
exposures of higher levels of radiation as long as it's carefully monitored. Lower levels can be tolerated for longer periods.
4. Dosimetry:If you work with radiation, you'll wear a dosimeter badge. It measures radiation exposure. A radiation safety officer keeps track of how much radiation people receive. If your exposure has been too high, you might be temporarily assigned to other duties.
