CBSE Class 10 Science Advanced Physics Source of Energy Nuclear Fission and Fusion Notes Set 01

Source of Energy, Nuclear Fission and Fusion

A. Sources of Energy

Energy and its sources

Energy is the ability of a body to do work. The energy stored in a system equals the total work it can deliver before it is fully used up. Most of our daily energy needs are met by fuels and electricity, and the energy stored in these fuels was originally collected from the Sun. Energy can change from one form to another.

The Sun, wind, hot rocks in the earth (geothermal), flowing water, coal, petrol, diesel, natural gas, biogas and many more are available to us as sources of energy. We use them for industry, trade and household work.

Types of sources

Renewable (non-conventional) sources are supplied continuously by nature and never get exhausted. Examples: the Sun (solar energy), ocean thermal energy, tidal energy, wind (kinetic energy), flowing water (hydro energy), wood.

Non-renewable (conventional) sources cannot be used again and again and will run out one day. Examples: coal, natural gas, petroleum and the other fossil fuels.

Qualities of a good source of energy

1. It should give a large amount of useful energy.
2. It should be easy to store in a small space.
3. It should be easy to transport.
4. It should supply energy steadily and regularly.

(a) Solar Energy

The Sun's heat is absorbed by land, mountains, rivers, lakes, seas and ponds. Plants use sunlight to prepare food by photosynthesis, and the same energy drives winds, rain, snowfall and sea waves. For this reason the Sun is called the everlasting (perennial) source of energy.

Important features of solar energy:

1. It reaches the earth in a very spread-out (diffused) form.
2. The top of the atmosphere receives about 1.3 kJ of energy per second on every square metre. Only about 47% of this reaches the ground, which is roughly 0.6 kJ per second per square metre.
3. The amount is not the same everywhere and it also changes from day to day and through the day at the same place.

Composition of sunlight

Ultraviolet (UV) rays are invisible rays with a wavelength shorter than that of violet light. They can be detected because they darken a photographic film and make fluorescent paper glow. They kill germs in food and drinking water. In excess they are harmful because they ionise matter and can cause skin cancer.

Visible light covers wavelengths from 400 nm (violet) to 700 nm (red). It is made up of seven colours, each with its own wavelength.

Infrared (IR) rays are invisible rays with a wavelength longer than that of red light. They produce heat in the object on which they fall, and a thermometer can detect them. About one-third of the solar energy is infrared. Every hot object gives out IR rays, and they are used for relief from body aches.

Uses of solar energy

1. Solar cookers cook food using sunlight.
2. Solar water heaters heat water.
3. Solar cells turn sunlight into electricity for watches, calculators and spacecraft experiments.
4. Green plants use it to make food by photosynthesis.
5. It dries clothes and food grains.
6. It is used to obtain salt from sea water.

Advantages

1. It is renewable and will not end, because nuclear fusion of hydrogen keeps taking place in the Sun's core.
2. It is available in huge quantity in every part of the world.
3. It causes no pollution.
4. It can be used in practical appliances.

Limitations

1. It is not available at night.
2. It is not equally available in all parts of the world.
3. It reaches us in a scattered, diffused form, so only a part of it can actually be used.
4. Clouds, fog, mist, haze and winds make the supply uneven.

Direct and indirect use of solar energy

Direct use: sunlight is collected as heat with the help of plane mirrors that send it on to black boxes holding uncooked food (solar cooker) or water (solar heater). Sunlight can also be turned straight into electricity in solar cells.

Indirect use: sunlight is first changed into another form, for example into chemical energy stored in the biomass of plants, or into the energy of sea waves, ocean heat and winds.

Solar heating devices

These devices collect and store the Sun's heat for heating and cooking. They are built to make the best use of solar heat in the following ways.

Reflectors: for moderate heating, plane mirrors reflect the sun's rays on to the device (solar cooker, solar water heater). For very high temperatures, concave mirrors are used so that the rays are focused.

Black paint: a black surface is a very good absorber and also a good emitter of heat, so painting the inside of the device black lets it absorb and store a large amount of heat over a large area.

Glass-sheet cover: the glass lets the shorter-wavelength infrared rays of sunlight enter the box but does not let the longer-wavelength infrared rays from the hot interior go out. The heat therefore stays trapped for a long time.

Greenhouse effect. Glass allows heat rays of short wavelength to pass in but stops heat rays of long wavelength from passing out. This trapping of heat by glass is known as the greenhouse effect.

(I) Box-type solar cooker

A solar cooker is a device that cooks food using solar energy. Its box is made of a poor conductor of heat such as plastic or fibre glass and is painted black on the inside. A plane mirror hinged to the lid is tilted until a strong beam of sunlight falls on the glass top. The rays pass through the glass, and the box and the containers absorb a large amount of infrared radiation. The temperature inside rises to about 100 °C to 130 °C.

Fig. 1: Box-type solar cooker

(II) Spherical-reflector (concentrating) solar cooker

This cooker has an insulated metal box painted black inside, but instead of a plane mirror it uses a spherical reflector, either concave or parabolic, because a very high temperature is needed. Sunlight falling on the reflector is concentrated at one point (the focus), where the temperature becomes very high. The vessel is therefore placed at the focus. Such a cooker can fry food and make chapatis.

Fig. 2: Spherical-reflector type solar cooker

Box-type and spherical-reflector cookers compared

(III) Solar cells

A solar cell is a device that changes sunlight directly into electricity. Because sunlight also carries light energy, solar cells are called photovoltaic cells, and producing electricity directly from sunlight is called the photovoltaic effect. It occurs when radiation falls on a suitable sensitive material and sets electrons flowing. The first cells, made with selenium, converted only 0.6% of the incident solar energy into electricity. Modern cells made from semiconductors convert 10% to 15%.

Semiconductors. Semiconductors conduct electricity only slightly; they are neither good conductors nor perfect insulators. Adding a small amount of a suitable impurity, called doping, raises their conductivity a great deal. Silicon doped with boron is hungry for electrons and is called p-type (acceptor); silicon doped with phosphorus has extra electrons and is called n-type (donor). Light falling on a semiconductor also raises its conductivity.

Working of a solar cell. Solar cells are usually made from silicon and gallium. Thin wafers of doped semiconductor are arranged so that, when light falls on them, a potential difference appears between two regions of the semiconductor. A cell of about 4 cm² area gives a potential difference of 0.4 V to 0.5 V and a current of about 60 mA.

Solar cell panel. A single cell gives very little power, so many cells are joined side by side in a fixed pattern. The combination, called a solar cell panel, gives a much larger voltage and current. Panels supply power to artificial satellites, street lights in remote places and irrigation pumps far from the grid. In a pumping set the panel's electricity is stored in a battery, the battery runs an electric motor, and the motor drives the pump that lifts underground water.

The cells of a panel are joined by silver wires, because silver is the best conductor and has the least resistance. This makes the panel costly but more efficient, since wires of any other metal would waste a noticeable part of the electricity in overcoming their resistance.

Fig. 3: Solar cell panel with storage cell

Uses of solar cells: power for artificial satellites and space probes; street lighting, traffic signals, water pumps, and radio and TV sets in remote areas of India; electricity for lighthouses at sea and offshore oil-drilling platforms; electronic watches and calculators.

Advantages: they use solar energy directly; they work even in diffused light; they need no maintenance; they cause no pollution.

Disadvantages: the stored battery energy is direct current (d.c.); where alternating current is needed it must be converted, which lowers efficiency and adds cost. They are expensive because the semiconductor material must be extremely pure.

(d) Wind Energy

Air in motion is wind. Like any moving body, moving air has kinetic energy and can do mechanical work. Wind energy is therefore the kinetic energy of a large mass of moving air.

How wind is produced. Solar energy is responsible for it. Sunlight is much stronger near the equator than near the poles, so the air near the ground at the equator becomes very hot. Being lighter, it rises, and cooler air from the polar regions flows in to fill the space it leaves. Thus air moves from regions of higher pressure to regions of lower pressure, and this flow of air is wind.

Advantages: it causes no pollution; it is free of cost; air is an inexhaustible, renewable source.

Disadvantages: wind is not available all the time; windmills and sailboats cannot work unless the wind is strong enough; wind speed changes with time and season; its energy can be used only at the place where it blows; nobody can guarantee wind when it is needed, since there is no place where the wind blows all the time; wind is hard to predict.

Devices that use wind energy

(I) Windmill. A windmill works on the energy of blowing air. It has large blades (vanes) that can turn about a horizontal axis and are mounted on top of a tall tower. Wind striking the blades turns them, so the kinetic energy of the wind becomes rotational energy of the blades, and this motion is passed to other parts for useful work.

In a water-pumping windmill the blades are fixed to one end of a shaft. The other end of the shaft is bent like an inverted V and joined to the free end of the pump rod. As the blades turn, the shaft turns the crank, the crank moves the piston rod of the pump up and down, and water is drawn from the well.

Fig. 4: Windmill for a water pump

(II) Windmill for a flour mill. Using toothed wheels and shafts, a windmill can also grind grain. The shaft joined to the blades carries a toothed wheel W₁. A second toothed wheel W₂ meshes with W₁ so that turning W₁ about a horizontal axis turns W₂ about a vertical axis. W₂ is fixed to a vertical shaft that rotates the upper, heavy millstone B above a fixed lower stone A. Grain fed between the stones is ground into flour. Thus the kinetic energy of the wind runs the flour mill.

Fig. 5: Windmill operating a flour mill

(III) Wind generator. A wind generator produces electricity from wind. Fast wind turns the blades of a wind turbine continuously, and the coil of a small electric generator is coupled to the turbine shaft, so electricity is generated. One turbine gives only a small output, so many turbines are put up over a large stretch of land. Such a group working together to produce electricity on a large scale is called a wind energy farm.

Fig. 6: Wind generator

(e) Hydro Energy

Flowing water carries a lot of kinetic energy, and this is called hydro energy. Water stored in dams at a height also holds energy, so the source is renewable, and it ultimately comes from solar energy (the Sun evaporates the water that falls again as rain). Hydro energy has been used for grinding grain, for irrigation and for floating logs of wood out of remote areas. On a large scale it is used in hydroelectric power stations.

A dam is built to store water. Water from the dam falls through pipes from a height and strikes the blades of huge turbines at the bottom. The turbine turns the coil of a generator, which produces electricity.

Fig. 7: Hydroelectric power plant

Advantages of hydel power: no pollution; the moving water costs nothing; it is a renewable source that never gets exhausted; dams on rivers help to control floods and provide water for irrigation.

Limitations: flowing water is available only near rivers; a reasonable amount of electricity needs fast-moving water in large quantity; a dam disturbs the ecological balance downstream; the soil downstream may become poorer because the yearly floods no longer deposit nutrient-rich silt on the river banks.

(f) Tidal Energy

The pull of the moon on sea water makes the sea surface rise and fall; these movements are called tidal waves, and the energy of the rising and falling water is tidal energy. A rise of the sea level is a high tide and a fall is a low tide. Tides come and go twice a day, and the enormous movement of water between high and low tide can generate a large amount of energy in coastal areas.

Harnessing tidal energy. A tidal barrage (tidal dam) is built across a narrow opening to the sea and a turbine is fixed in the opening. At high tide, sea water flows into the reservoir behind the barrage and turns the turbine to produce electricity. At low tide, the water stored in the reservoir flows back out to the sea and again turns the turbine.

Fig. 8: Tidal barrage: (a) at high tide, water flows from the sea into the reservoir and turns the turbine; (b) at low tide, stored water flows out into the sea and turns the turbine

Limitations: the difference between high and low tide is not large enough to generate electricity on a big scale, and there are very few places where such a barrage can be built. For these reasons tidal energy is unlikely to become a major source of energy.

Locations in India: the Gulf of Kutch in Gujarat and the Sundarbans in West Bengal.

(g) Sea-Wave Energy

Wind blowing over the ocean sets up fast-moving waves, and because of their speed they carry a lot of kinetic energy that can be used to make electricity. Two ideas are used:

1. Floating generators set up in the sea move up and down with the waves, and this movement drives the generators.
2. Waves move up and down inside large tubes and compress the air in them. The compressed air turns the turbine of a generator.

(h) Ocean Thermal Energy

The surface water of the ocean is warmer than the water at great depth. The energy that can be drawn from this temperature difference is called ocean thermal energy.

Harnessing it. Plants called OTEC (Ocean Thermal Energy Conversion) power plants do this. An OTEC plant works efficiently only if the surface water is at least 20 °C warmer than the water at a depth of about 1000 m.

Fig. 9: OTEC power plant using ammonia

Warm surface water boils a liquid such as ammonia (or a chlorofluorocarbon) in a heat exchanger (evaporator). The vapour runs the turbine, which drives the generator. Cold water pumped up from the depths cools the vapour in a second heat exchanger (condenser) and turns it back into liquid, which is pumped to the evaporator again, and the cycle repeats.

Advantages: it can be used round the clock throughout the year; it is renewable and causes no pollution.

(i) Ocean-Wave Energy

The energy carried by ocean waves is called ocean-wave energy. Wind blowing across the ocean makes the waves, and the kinetic energy of the huge mass of water moving with them is the ocean-wave energy. In another development the electricity made is used to split water into hydrogen and oxygen, and the hydrogen is piped to the shore.

Two common devices are (I) surface followers (floats or pitching devices) and (II) oscillating water columns (OWC).

(I) Surface follower. A row of floating objects is pivoted on a rigid shaft along the coast. As the waves lift and lower the floats, mechanical energy is produced in the shaft and is changed into electricity.

Fig. 10: A surface follower used to harness ocean energy

(II) Oscillating water column. The force of waves entering a fixed device does mechanical work or generates electricity. In anchored navigation buoys, for instance, the waves compress the air, and the compressed air turns a turbine to generate electricity.

Fig. 11: An oscillating water column wave power generator

(j) Geothermal Energy

Geothermal energy is the heat of hot rocks deep inside the earth, and it can be used to make electricity. It is one of the few sources of energy that does not come, directly or indirectly, from the Sun. Places where very hot rocks lie at a certain depth below the surface are called hot spots, and they are the sources of geothermal energy.

It is harnessed in two ways:

1. Very hot rocks heat underground water into steam. As more steam collects among the rocks it becomes compressed to a high pressure. A hole is drilled to the hot rocks and the high-pressure steam rushes up the pipe to turn the turbine of a generator.
2. In some places the rocks have openings through which steam and hot water gush out naturally, like a geyser. The steam turns turbines to produce electricity, and the hot water can be used to cook food.

(k) Bio Energy

The energy obtained from the biomass of plants and animals is bio energy. Biomass is renewable because plants and animals are produced again and again. Biomass means the waste and dead parts of living things, such as cattle dung, wood, sewage and farm wastes (crop residues) like bagasse, the fibre left after the juice of sugar cane has been pressed out. Biomass consists of carbon compounds and is the oldest source of heat for homes. It can be used in two ways: the dry biomass (dung cake, wood) can be burnt directly, or it can first be converted into better fuels, which are then burnt.

Biogas. The breakdown of organic matter in the absence of oxygen is called anaerobic degradation, and it is carried out by anaerobic bacteria. Biogas is formed when animal waste such as dung is degraded this way in the presence of water. It is a mixture of methane, carbon dioxide, hydrogen and hydrogen sulphide, and its main component is methane.

Biogas plant. Biogas is made in a biogas plant from a mixture of cattle dung and water. There are two types: (I) floating gas-holder type and (II) fixed-dome type. The raw material is the same in both.

Fig. 12: Fixed-dome type biogas plant

Parts of a fixed-dome plant.

1. Digester: a well-like brick chamber whose dome-shaped roof is a fixed tank for storing the gas. A pipe at the top of the dome takes the gas out.
2. Mixing tank: built above ground level at one side of the digester.
3. Inlet tank: below ground level, under the mixing tank.
4. Overflow tank: built on the other side of the digester at a level lower than the mixing tank.
5. Outlet tank: below ground level, under the overflow tank.

The mixing tank is joined to the inlet tank and the overflow tank is joined to the outlet tank.

Working. Cattle dung (sometimes also human waste and household sewage) is mixed with an equal amount of water in the mixing tank to form a slurry. In the digester, anaerobic bacteria ferment the slurry and form biogas, which collects in the dome. As more gas collects it presses on the slurry and pushes the used slurry out into the outlet tank and from there to the overflow tank. The used slurry is rich in nitrogen and phosphorus compounds and is an excellent manure. The gas leaves through the outlet pipe at the top of the dome, which has a gas control valve, and is distributed as needed. Fresh slurry is fed in regularly, so biogas is obtained continuously.

Uses of biogas: cooking fuel (in smokeless chulhas) and other heating; running engines and water-pumping sets; street lighting in villages.

Advantages of using household sewage to make biogas: it gives a smokeless fuel; the spent slurry is a good manure; it helps to control water pollution by breaking down waste.

Merits of biogas as a fuel: it is clean, with no smoke or pollution; it has a high calorific value; it is cheap; it is convenient to use; it needs no storage space at home because it is piped from the plant.

(l) Fuels

A fuel is a substance that gives out energy, as heat and light, when it burns in oxygen. Examples: wood, gas, petrol, kerosene, diesel, coal and animal waste. Fuels are combustible substances.

Characteristics of a good fuel

1. High calorific value.
2. A suitable ignition temperature, so that it catches fire easily.
3. Little or no residue (ash) after burning.
4. It should burn smoothly at a moderate, steady rate.
5. It should not be more valuable for some other use. Coke, for example, is a good fuel but is worth more as a reducing agent in extracting metals.
6. It should be cheap and easily available.
7. It should be easy to handle, safe to carry and convenient to store.

Types of fuels

Solid fuels: wood, charcoal, coke, coal, paraffin and tallow. Wood was the first solid fuel used by humans, and paraffin and tallow are used for candles.
Liquid fuels: petrol, kerosene, diesel and methanol. Most of them come from petroleum. They leave no solid residue and are easy to store.
Gaseous fuels: natural gas, coal gas, producer gas, water gas and liquefied petroleum gas (LPG).

Fossil fuels

Fossil fuels are the remains of animals and plants of prehistoric times that were buried under the earth millions of years ago. Coal, petroleum and natural gas are fossil fuels. They formed in the absence of oxygen, as pressure, heat and bacteria slowly changed the buried remains. It was the sunlight of that time that made the plants grow, so fossil fuels are energy-rich carbon compounds originally made by plants with the help of the Sun's energy.

Calorific value

All fuels give heat on burning, but in different amounts. A fuel's usefulness is measured by its calorific value: the heat produced by completely burning a unit mass of the fuel. In practice the unit mass is 1 gram, so the calorific value is the heat given out when 1 g of the fuel burns completely. For instance, 1 g of charcoal gives 33000 J, so its calorific value is 33000 J/g. As the joule is small, the value is usually written in kilojoules per gram (kJ/g), the unit in which calorific values are normally quoted.

Calorific values of some common fuels

Among common elements, hydrogen has the highest calorific value, so a fuel with a larger percentage of hydrogen has a higher calorific value than one with less. Wood is made of carbohydrates such as cellulose, \( (\mathrm{C_6H_{10}O_5})_n \). On burning, only the carbon and hydrogen in it produce heat; the oxygen only helps burning. Since wood has a comparatively small share of carbon and hydrogen, its calorific value is low. In general, fuels that contain oxygen burn readily but give less heat per unit mass.

Solved Examples

Illustration 1. A concentrator-type solar water heater has a surface area of 5 m² and it can absorb 80% of the incident solar radiation falling on it, while it reflects the rest. Calculate the energy concentrated by the heater at its focus in a time period of 2 hrs, if solar energy incident on it is at the rate of 0.4 kJ/m²s.
Answer:
Area A = 5 m², time t = 2 h = 7200 s, incident rate = 0.4 kJ/m²s.
The mirror absorbs 80%; the remaining 20% is reflected and is the part that is concentrated at the focus.
Energy at the focus = rate × A × t × \( \frac{20}{100} \) = 0.4 × 5 × 7200 × 0.2 = 2880 kJ.

B. Nuclear Energy

The energy released when changes take place in the nucleus of an atom is called nuclear energy.

Nature of nuclear energy: it is partly renewable and partly non-renewable. Nuclear fusion is a renewable route because the hydrogen it needs is plentiful in nature, while nuclear fission is non-renewable because the uranium it needs is available only in limited amount.

(a) Binding Energy

Protons and neutrons in the nucleus are called nucleons. One would expect the mass of a nucleus to equal the sum of the masses of its nucleons, but the actual nuclear mass is slightly smaller. The difference between the expected mass (sum of the masses of the separate nucleons) and the actual nuclear mass is the mass defect. By Einstein's equation \( E = mc^2 \) the mass defect is equivalent to energy.

The energy equivalent to the mass defect, which holds the nucleons together, is called the binding energy of the nucleus. It is also the energy needed to pull all the nucleons of the nucleus apart. The binding energy per nucleon is a measure of how stable the nucleus is.

The mass defect (in atomic mass units) is found from

\[ \Delta m = [\,Z m_p + (A - Z)\, m_n\,] - m_N \]

where Z is the atomic number, A is the mass number, \( m_p \) is the mass of a proton, \( m_n \) is the mass of a neutron and \( m_N \) is the mass of the nucleus.

(b) Nuclear Reactions

In a nuclear reaction the nucleus of an atom changes, forming new atoms and releasing a tremendous amount of energy. A nuclear reaction can turn one element into another, which a chemical reaction can never do. Some nuclear reactions occur by themselves in nature as nuclei try to become stable; this is radioactivity. Nuclear reactions can also be produced artificially to obtain large amounts of energy. They are of two kinds: nuclear fission and nuclear fusion.

(i) Nuclear fission

In 1939 the German scientists Otto Hahn and Fritz Strassmann analysed the products formed when uranium is bombarded with neutrons. One product was an isotope of barium that emits beta rays and has a half-life of 86 minutes, matching the known properties of \( {}^{139}\mathrm{Ba} \). Another was an isotope of lanthanum, \( {}^{140}\mathrm{La} \), with a half-life of 40 hours. Uranium (Z = 92, mass number 235) had broken into barium (Z = 56, mass number 139) and lanthanum (Z = 57, mass number 140). The two products together have mass number 279, which is more than that of uranium, so both cannot arise from one nucleus in a single reaction; the other partner must have an atomic number of about 36 and a mass number of about 100. Hahn and Strassmann did find active isotopes of strontium (\( {}_{38}\mathrm{Sr} \)) and yttrium (\( {}_{39}\mathrm{Y} \)). In simple words, they showed that heavy uranium nuclei split into lighter nuclei of smaller atomic numbers. This process is called nuclear fission.

(I) Fission products. Fission of uranium gives nuclei with mass numbers from 72 (\( {}^{72}_{30}\mathrm{Zn} \)) to 158 (\( {}^{158}_{63}\mathrm{Eu} \)). Fission of \( {}^{235}_{92}\mathrm{U} \) mainly gives two groups: a light group with mass numbers 85 to 104 and a heavy group with mass numbers 130 to 149. The most common products are molybdenum (\( {}_{42}\mathrm{Mo} \)) and lanthanum (\( {}_{57}\mathrm{La} \)). Fission can be prompt or delayed. In prompt fission the nucleus splits at once when a projectile of suitable energy strikes it. In delayed fission the projectile enters the nucleus and makes it unstable, so that the nucleus (now \( {}^{236}_{92}\mathrm{U} \)) splits a little later. Natural uranium and some other isotopes also undergo fission without being hit by any projectile.

(II) Types of fission reactions. There are three kinds.

1. Spontaneous fission: the nucleus splits on its own, without being struck by a projectile such as a neutron. The natural shaking (oscillation) of the nucleons in a heavy nucleus makes it break up. It goes on all the time in natural uranium, but at a very, very slow rate.
2. Prompt fission: the nucleus splits into smaller nuclei instantly when a projectile such as a neutron hits it. About 99% of the fission of uranium-235 caused by slow neutrons is prompt, and it is brought about by prompt neutrons emitted at once by the splitting nuclei.
3. Delayed fission: a neutron enters the nucleus and makes it unstable, and the nucleus splits after a short while. About 1% of the neutron-induced fission of uranium-235 is delayed, and it is caused by delayed neutrons, which come out slowly from the splitting nuclei.

Different isotopes need different amounts of energy for fission, and below a certain threshold energy of the projectile no fission occurs. Fission is usually accompanied by the emission of neutrons that cause further fission; the fission of uranium releases 2 or 3 neutrons each time, with energies spread over a wide range. In nuclear reactions energy is usually measured in eV or MeV:

\[ 1\ \mathrm{eV} = 1.6 \times 10^{-19}\ \mathrm{J}, \qquad 1\ \mathrm{MeV} = 1.6 \times 10^{-13}\ \mathrm{J} \]

(III) Energy released in fission. It is calculated by comparing the total mass of the nucleus that undergoes fission plus the projectile with the total mass of the fission products.

Worked examples on fission energy

Illustration 2. Fission of \( {}^{235}_{92}\mathrm{U} \) takes place when it is hit by slow (low-energy) neutrons of about 0.025 eV, which move at about 2200 m/s, roughly ten times the speed of a modern jet plane. Many fission reactions are possible. Consider the most probable one, producing \( {}^{95}\mathrm{Mo} \) and \( {}^{139}_{57}\mathrm{La} \) and 2 neutrons:

\[ {}^{235}_{92}\mathrm{U} + {}^{1}_{0}\mathrm{n} \rightarrow {}^{95}_{42}\mathrm{Mo} + {}^{139}_{57}\mathrm{La} + 2\,{}^{1}_{0}\mathrm{n} + 7\,{}^{0}_{-1}\mathrm{e} + \text{Energy} \]

(The atomic number of molybdenum here is 42; the seven electrons, which have negligible mass, balance the charge.)

Mass of \( {}^{235}_{92}\mathrm{U} \) = 235.124 amu; mass of one neutron = 1.009 amu. Initial mass = 236.133 amu ... (i)
Mass of \( {}^{95}\mathrm{Mo} \) = 94.946 amu; mass of \( {}^{139}\mathrm{La} \) = 138.955 amu; mass of 2 neutrons = 2.018 amu. Final mass = 235.919 amu ... (ii)
Mass defect = (i) − (ii) = 236.133 − 235.919 = 0.214 amu.
Since 1 amu (1 u) is equivalent to 931 MeV, energy released = 0.214 × 931 = 199.234 ≈ 199.2 MeV.

Illustration 3. Another common fission reaction of \( {}^{235}_{92}\mathrm{U} \):

\[ {}^{235}_{92}\mathrm{U} + {}^{1}_{0}\mathrm{n} \rightarrow {}^{92}_{36}\mathrm{Kr} + {}^{141}_{56}\mathrm{Ba} + 3\,{}^{1}_{0}\mathrm{n} + \text{Energy} \]

Initial mass = 235.0439 + 1.0087 = 236.0526 amu.
Final mass = 91.8954 + 140.9177 + 3 × 1.0087 (= 3.0261) = 235.8392 u.
Mass defect = 236.0526 − 235.8392 = 0.2134 amu.
Energy produced = 0.2134 × 931 = 198.7 MeV (about 200 MeV).

Illustration 4. Energy produced by the complete fission of 1 kg of \( {}^{235}_{92}\mathrm{U} \).

235 g of uranium-235 contains \( 6.023 \times 10^{23} \) atoms, so the number of atoms in 1 kg (1000 g) is

\[ \frac{6.023 \times 10^{23}}{235} \times 1000 = 25.63 \times 10^{23} = 2.563 \times 10^{24}\ \text{atoms} \]

If each atom releases 200 MeV, the energy released by 1 kg is

\[ 25.63 \times 10^{23} \times 200\ \mathrm{MeV} = 5.126 \times 10^{26}\ \mathrm{MeV} = 5.126 \times 10^{26} \times 1.6 \times 10^{-13}\ \mathrm{J} \approx 8.2 \times 10^{13}\ \mathrm{J} \]

This equals the energy obtained by burning about 2500 tonnes of coal.

(IV) Process of nuclear fission: the liquid-drop model. The liquid-drop model of the nucleus, proposed by Yakov Frenkel, Niels Bohr and John Wheeler, explains fission. A drop of water becomes unstable if a small drop strikes it, and in the same way a uranium nucleus becomes unstable and breaks when a neutron hits it. In this model the nucleus is treated as an incompressible liquid drop with uniform positive charge, held together by a stretchable skin-like membrane that encloses all the protons and neutrons. In its stable state the nucleus, like a water drop, is spherical.

Liquid-drop model of fission: (a) spherical nucleus, (b) waist develops, (c) neck develops, then fission

In (a) the nucleus is spherical. Its nucleons are so close that the attractive nuclear force and the repulsive electrostatic force are delicately balanced. When a slow neutron enters the uranium-235 nucleus, the balance is upset. The neutron's energy is shared among the nucleons, which begin to oscillate more and more, stretching the skin so that the nucleus elongates and a waist forms (b). As the nucleons move apart, the nuclear attraction between them weakens, and the electrostatic repulsion between the protons becomes dominant. A neck forms (c), which weakens the nuclear force still further, and the growing repulsion finally breaks the nucleus into two smaller nuclei, barium-139 and krypton-94, and three neutrons are released.

(V) Chain reaction. A reaction in which the particle that starts it is also produced during the reaction, so that the reaction keeps going by itself, is a chain reaction. It continues until one of the reactants is used up. The fission of uranium-235 by slow neutrons is a chain reaction because neutrons start it and neutrons are also produced by it. The neutrons from the fission of one uranium atom cause the fission of more uranium atoms, and so on like an unending chain, with a large release of energy at every step.

Fig. 13: Chain reaction in uranium-235

In each fission only 1 neutron is used up but 3 are produced, so the process is self-sustaining. If, on average, fewer than 1 neutron were produced per fission, the reaction would die out like a fire in wet fuel. A chain reaction needs a large number of uranium atoms, so it cannot take place in a very small lump of uranium-235 but only in a sufficiently large mass. The smallest mass of uranium-235 (or any other fissionable material) that can sustain a chain reaction is called its critical mass.

(ii) Nuclear fusion

Under special conditions the nuclei of light elements can join to form a nucleus of higher atomic number. For example, two deuterons can combine to form a \( {}^{3}_{2}\mathrm{He} \) nucleus and a neutron. The deuteron (d) is the nucleus of heavy hydrogen \( {}^{2}_{1}\mathrm{H} \), made of one proton and one neutron. The process in which nuclei of low atomic number combine to form a heavier nucleus is called nuclear fusion. Like fission, fusion releases energy. It was discovered in the 1930s. Typical fusion reactions are:

\[ d + d \rightarrow {}^{3}_{2}\mathrm{He} + n + 3.3\ \mathrm{MeV} \qquad \ldots (i) \]

\[ d + d \rightarrow t + p + 4.0\ \mathrm{MeV} \qquad \ldots (ii) \]

Here t is a triton, the nucleus of the heavy isotope \( {}^{3}_{1}\mathrm{H} \) (one proton and two neutrons), and p is a proton. So two deuterons can fuse to give either helium-3 and a neutron, or a triton and a proton. Another important kind of fusion involves the conversion of protons and neutrons into each other. The simplest is the formation of a deuteron from hydrogen:

\[ p + p \rightarrow d + e^{+} + \nu \qquad \ldots (iii) \]

One of the two protons changes into a neutron to form a deuteron, and at the same time a positron \( e^{+} \) (like an electron but positively charged) and a neutrino \( \nu \) are created. The neutrino is a neutral particle of negligible mass and very great penetrating power.

Fusion has been seen in many light nuclides. In the laboratory it can be produced by accelerating light nuclei in a particle accelerator and letting these high-energy projectiles strike a target whose nuclei can fuse with them. Deuterons have enough kinetic energy to fuse at a temperature of about \( 10^{6} \) K.

Nuclei that fuse must overcome the huge electrostatic repulsion between them at extremely small distances. This is possible if the thermal kinetic energy is raised by heating to millions of kelvin. At such temperatures atoms are completely ionised, and the material is a mixture of electrons and nuclei moving at high speed. Matter in this state, with equal amounts of positive and negative charge, is called a plasma. Fusion under these conditions is called a thermonuclear reaction. In 1939 Hans Bethe proposed that the enormous energy of the Sun comes from thermonuclear reactions, and this is now universally accepted.

(c) Secret of the Sun's Energy

The Sun is a huge ball of hydrogen at extremely high temperature. Hydrogen nuclei in it collide and fuse to form helium, and every such fusion releases tremendous energy as heat and light. That energy is what makes the Sun shine. The book gives the main reaction as the fusion of two deuterons:

\[ {}^{2}_{1}\mathrm{H} + {}^{2}_{1}\mathrm{H} \xrightarrow{\text{fusion}} {}^{4}_{2}\mathrm{He} + \text{enormous energy} \]

(deuteron = heavy hydrogen; helium nucleus). The Sun also contains the other two isotopes of hydrogen: ordinary hydrogen \( {}^{1}_{1}\mathrm{H} \) (protium) and very heavy hydrogen \( {}^{3}_{1}\mathrm{H} \) (tritium). These also fuse with deuterium to give helium and energy:

\[ {}^{1}_{1}\mathrm{H} + {}^{2}_{1}\mathrm{H} \rightarrow {}^{3}_{2}\mathrm{He} + \text{large amount of energy} \]

\[ {}^{2}_{1}\mathrm{H} + {}^{3}_{1}\mathrm{H} \rightarrow {}^{4}_{2}\mathrm{He} + {}^{1}_{0}\mathrm{n} + \text{large amount of energy} \]

Fusion of the isotopes of hydrogen into helium is going on all the time inside the Sun, and the energy produced is radiated as light of many wavelengths. It is the infrared radiation among them that carries heat and warms the earth.

(d) Hydrogen Bomb

The hydrogen bomb works on nuclear fusion: it is an uncontrolled nuclear fusion process. A fission arrangement sits at the centre and is surrounded by a mixture of deuterium (\( {}^{2}_{1}\mathrm{H} \)) and lithium-6 (\( {}^{6}_{3}\mathrm{Li} \)). The fission gives the heat and neutrons. The neutrons change lithium-6 into tritium, and the heat starts the fusion of \( {}^{2}_{1}\mathrm{H} \) with \( {}^{3}_{1}\mathrm{H} \), which then releases a large amount of energy. Because fusion needs very high temperature, these are called thermonuclear reactions and the bomb is a thermonuclear bomb. The reactions are:

Fission at the centre \( \rightarrow \) heat + neutrons

\[ {}^{6}_{3}\mathrm{Li} + {}^{1}_{0}\mathrm{n} \rightarrow {}^{3}_{1}\mathrm{H} + {}^{4}_{2}\mathrm{He} + \text{energy} \]

\[ {}^{2}_{1}\mathrm{H} + {}^{3}_{1}\mathrm{H} \rightarrow {}^{4}_{2}\mathrm{He} + {}^{1}_{0}\mathrm{n} + \text{energy} \]

\[ {}^{2}_{1}\mathrm{H} + {}^{2}_{1}\mathrm{H} \rightarrow {}^{4}_{2}\mathrm{He} + \text{energy} \]

\[ {}^{3}_{1}\mathrm{H} + {}^{3}_{1}\mathrm{H} \rightarrow {}^{4}_{2}\mathrm{He} + 2\,{}^{1}_{0}\mathrm{n} + \text{energy} \]

Tritium is unstable, so it has to be produced inside the bomb itself (from lithium-6) and not stored.

Facts about the hydrogen (thermonuclear) bomb, as listed in the book:

1. Five countries have tested it:

2. Four other countries that are not signatories of the NPT (Nuclear Non-Proliferation Treaty) are believed to possess the bomb; the book lists India (May 1998), Pakistan (May 1998) and North Korea (6 January 2016).

The most powerful hydrogen bomb ever exploded was the Tsar Bomba, tested by the Soviet Union (Russia) in 1961.

(e) Difference between Nuclear Fission and Nuclear Fusion