Physics Topics such as mechanics, thermodynamics, and electromagnetism are fundamental to many other scientific fields.
What is the Definition of a Chain Reaction? What is used for Controlling Fission?
Peripheral reactions: In most of the nuclear reactions, the emitted particle is not heavier than a projectile particle. This indicates that there is a small change in atomic number and mass number of the target nucleus. These are termed peripheral reactions because the core of the nucleus is practically unaffected. For example,
7N14 + 2He4 → 8O17; 1H1 ; 7N14 + 0n1 → 6C14 + 1H1
Collision of thermal neutron with U-235: This results in the formation of almost two equally heavy nuclei, due to the disintegration of the heavier U-235 nucleus. For example,
0n1 + 92U235 → 35Br85 + 57La148 + 30n1 ……. (1)
0n1 + 92U235 → 36Kr92 + 56Ba141 + 30n1 ……. (2)
Such splitting up of the nucleus cannot be termed peripheral reaction. Generally it is called nuclear fission. This was invented in 1939 by Otto Han and Strassman.
Definition: Breaking up of a heavy nucleus into two nuclei of almost equal masses is called nuclear fission.
Energy released in nuclear fission: Mass lost during nuclear fission changes to energy as per mass-energy equivalence. In the equation (1),
Initial mass = total mass of U-235 and neutron
= 235.1 + 1.009 = 236.1 u (approx.)
Final mass = total mass of Br-85, La-148 and 3 neutrons
= 84.9 + 148.0 + 3 × 1.009 = 235.9 u (approx.)
∴ Mass loss = 236.1 – 235.9 = 0.2u
∴ Energy released = 0.2 × 931 MeV = 186 MeV (approx.) (as 1 u ≈ 931 MeV). This energy is available from only one nucleus of U-235.
Considering the number of atoms of U-235 in 1 g of U-235, the energy released during nuclear fission is of the order of 7.6 × 1010 J per g. This energy is equivalent to the energy that can be obtained by burning 3000 tons of coal.
Moderator: The three neutrons released in nuclear fission practically absorb the released energy (approximately 186 MeV) and change to high speed neutrons as kinetic energy increases. For further use of these neutrons for fission reaction, these are to be slowed down as thermal neutrons. Substances like heavy water (D2O), graphite can slow down the high speed neutrons when neutrons pass through them. These are called moderators.
Chain reaction: Nuclear reactions sustained by the product of Initial reaction leading from one reaction to the other consecutively, is called chain reaction. In equation (1), one neutron is bombarded on U-235 target and 3 neutrons are released. They are slowed down to thermal neutron. Now they are used to set up further fission of 3 U-235 nuclei, releasing 9 new neutrons and so on. The number of fissions, like 1, 3, 9, 27, 81, ….. is increasing in the form of a multiple progression.
Hence, in a small time a large number of fissions take place, releasing a huge amount of thermal energy. This is the principle of an atom bomb.
Critical size: Neutrons formed during fission have a tendency to escape without hitting the target nucleus. This decreases the number of available neutrons to sustain the chain reaction, ultimately resulting in the cessation of the chain reaction. To prevent this, the following two methods are applied-
- The radioactive sample that is taken is in the shape of a sphere, which has less surface area compared to its volume.
- Mass of sample taken is a little more than the calculated value. To continue a nuclear fission sustaining its chain reaction the minimum size of sample required, is called critical size.
Controlled fission: Nuclear reactor: The energy released during nuclear fission should not be misused. Rather it should be used for useful and necessary purposes like generation of electricity, but for that the following precautions should be taken:
1. the huge energy produced should not go out of control causing immense destruction and
2. energy supply should continue almost at the same rate for a long time. Fission brought about conforming to the above two conditions is called controlled chain reaction or controlled fission. The device where controlled fission and subsequent generation of electricity is conducted is called nuclear reactor.
The effective number of fission neutrons produced per absorption in the fuel in each successive step of a chain reaction is called neutron reproduction factor. In case of uncontrolled chain reaction in atom bomb, the ratio is 2.5 or above. In a nuclear reactor, the factor is kept close to 1 or slightly more to attain condition
- and
- stated above. This is the guiding principle of an atomic reactor.
Out of different types of reactors, Pressurised Water Reactor or PWR is most widely used.
A schematic diagram of a PWR is shown in Fig. The reactor consists of—
Core: Inside the core the nuclear reaction takes place. Core contains
1. fuel rod,
2. control rod,
3. moderator and
4. coolant.
- U-235 is used as fuel rod. Heat is generated when U-235 is bombarded with neutrons.
- Steel rod with a coating of boron is used as control rod. Boron absorbs surplus thermal neutrons.
- Heavy water is usually used as moderator. Moderator slows down the high energy neutrons produced due to the nuclear reaction in the core to thermal neutrons to sustain the chain reaction.
- Generally water is used as coolant. Heat generated due to fission is absorbed by coolant water maintained at high pressure to avoid boiling.
Heat exchanger: In this part, heat from coolant water which is radioactive is transferred to non-radioactive water for further use. Radioactive water from coolant is kept confined within the core area by a protective concrete shielding.
Turbine: Non-radioactive water, at high temperature, is piped out of the shielding and converted to steam to rotate the turbine to produce electricity in the same manner as in a Thermal Power Station.
Numerical Examples
Example 1.
The kinetic energy of a slow moving neutron is 0.04 eV. What fraction of the speed of light is the speed of this neutron? At what temperature will the average kinetic energy of a gas molecule be equal to the energy of this neutron? [mass of neutron: 1.675 × 10-27 kg, Boltzmann constant, kB = 1.38 × 10-23JᐧK-1
Solution:
Kinetic energy of the slow neutron
= 0.04 eV = 0.04 × (1.6 × 10-19)
Kinetic energy, Ek = \(\frac{1}{2}\)mv2
or, v = \(\sqrt{\frac{2 E_k}{m}}\) = \(\sqrt{\frac{2 \times 0.04 \times 1.6 \times 10^{-19}}{1.675 \times 10^{-27}}}\)
= 2764 m ᐧ s-1
∴ \(\frac{v}{c}\) = \(\frac{2764}{3 \times 10^8}\) × 100% = 0.00092%
Average kinetic energy at temperature T
= \(\frac{3}{2}\)kBT = 0.04 × (1.6 × 10-19) J
∴ T = \(\frac{2 \times 0.04 \times\left(1.6 \times 10^{-19}\right)}{3 \times\left(1.38 \times 10^{-23}\right)}\) = 309 K = 36° C
Example 2.
In a typical nuclear fission reaction, it was found that there was a loss of mass of 0.2150 u. How much energy in MeV will be released from this reaction? [WBCHSE Sample Question]
Solution:
Loss of mass,
Δm = 0.2150 u = 0.2150 × (1.66 × 10-27) kg
Associated release of energy,
ΔE = Δm ᐧ c2
= 0.2150 × (1.66 × 10-27) × (3 × 108)2
= 3.2121 × 10-11J = \(\frac{3.2121 \times 10^{-11}}{1.6 \times 10^{-19}}\)eV
= 200 × 106 eV = 200 MeV