Nuclear Reactions
A nuclear reaction is a process in which an atomic nucleus interacts with another nucleus or with a nuclear particle, resulting in the formation of one or more new nuclei or particles.
In a nuclear reaction, the identity of the nucleus may change because the numbers of protons and neutrons can be altered. Nuclear reactions can occur naturally or can be induced artificially by bombarding a nucleus with particles such as neutrons, protons, alpha particles, or other nuclei.
A nuclear reaction is generally represented as
\( {}^{A}_{Z}X + {}^{a}_{z}x \rightarrow {}^{B}_{Y}Y + {}^{b}_{y}y \)
Here, \(X\) is the target nucleus, \(x\) is the incident particle, and \(Y\) and \(y\) are the products of the nuclear reaction.
Conservation Laws in Nuclear Reactions
Nuclear reactions obey several fundamental conservation laws. The most important conservation laws used in nuclear reactions are conservation of nucleon number, conservation of electric charge, conservation of energy, and conservation of momentum.
Conservation of Nucleon Number
The total number of nucleons, that is, protons and neutrons together, remains conserved in an ordinary nuclear reaction.
\[ A_1 + A_2 = A_3 + A_4 \]
where \(A\) represents the mass number of the corresponding nucleus or particle.
For example, consider the nuclear reaction
\[ {}^{14}_{7}\mathrm{N} + {}^{4}_{2}\mathrm{He} \rightarrow {}^{17}_{8}\mathrm{O} + {}^{1}_{1}\mathrm{H} \]
The total mass number before the reaction is \(14+4=18\), and after the reaction it is \(17+1=18\). Thus, the nucleon number is conserved.
Conservation of Electric Charge
The total electric charge before a nuclear reaction is equal to the total electric charge after the reaction.
\[ Z_1 + Z_2 = Z_3 + Z_4 \]
For the reaction
\[ {}^{14}_{7}\mathrm{N} + {}^{4}_{2}\mathrm{He} \rightarrow {}^{17}_{8}\mathrm{O} + {}^{1}_{1}\mathrm{H} \]
the total atomic number before the reaction is \(7+2=9\), while after the reaction it is \(8+1=9\). Therefore, electric charge is conserved.
Conservation of Energy
Energy is conserved in a nuclear reaction. However, nuclear reactions can involve conversion between mass and energy. The change in mass is related to the corresponding change in energy by Einstein’s mass-energy relation:
\[ E=mc^2 \]
Therefore, the total energy before and after the reaction remains conserved when the rest-mass energy and kinetic energy of all particles are taken into account.
Q-Value of a Nuclear Reaction
The Q-value of a nuclear reaction is the net energy released or absorbed during the reaction.
\[ Q=(\text{Total mass before reaction}-\text{Total mass after reaction})c^2 \]
If the masses are expressed in atomic mass units \(u\), the Q-value can be calculated using
\[ Q=\Delta m \times 931.5\ \mathrm{MeV} \]
where \(\Delta m\) is the mass difference in atomic mass units.
If \(Q>0\), energy is released and the reaction is called an exoergic nuclear reaction. If \(Q<0\), energy is absorbed and the reaction is called an endoergic nuclear reaction.
Example of a Nuclear Reaction
A well-known example is the bombardment of nitrogen-14 by an alpha particle:
\[ {}^{14}_{7}\mathrm{N}+{}^{4}_{2}\mathrm{He} \rightarrow {}^{17}_{8}\mathrm{O}+{}^{1}_{1}\mathrm{H} \]
In this reaction, the nitrogen nucleus is transformed into an oxygen nucleus and a proton is emitted. Thus, the reaction changes one element into another. Such a process is called artificial transmutation of elements, which is discussed in the next topic.
Thus, nuclear reactions involve changes in atomic nuclei while obeying fundamental conservation laws such as conservation of nucleon number, electric charge, energy, and momentum.
Artificial Transmutation of Elements
Artificial transmutation of elements is the process of changing the nucleus of one element into the nucleus of another element by bombarding it with suitable nuclear particles.
In an artificial transmutation, a stable or radioactive nucleus is deliberately bombarded with a suitable particle such as an alpha particle, proton, neutron, or other nucleus. The incident particle interacts with the target nucleus and produces a new nucleus along with one or more emitted particles.
The process is called artificial because the transformation is induced by deliberately causing a nuclear reaction rather than allowing the nucleus to undergo spontaneous radioactive decay.
Principle of Artificial Transmutation
The basic principle of artificial transmutation is to bombard a suitable target nucleus with a sufficiently energetic particle so that a nuclear reaction takes place and a nucleus of a different element is produced.
The general form of an artificial transmutation reaction can be written as
\[ {}^{A}_{Z}X+{}^{a}_{z}x \rightarrow {}^{B}_{Y}Y+{}^{b}_{y}y \]
Here, \( {}^{A}_{Z}X \) is the target nucleus, \( {}^{a}_{z}x \) is the incident particle, \( {}^{B}_{Y}Y \) is the new nucleus, and \( {}^{b}_{y}y \) is the emitted particle.
The reaction must satisfy the conservation of mass number and electric charge:
\[ A+a=B+b \]
\[ Z+z=Y+y \]
Rutherford’s Experiment on Artificial Transmutation
The first successful artificial transmutation of an element was achieved by Ernest Rutherford in 1919. He bombarded nitrogen gas with high-energy alpha particles emitted by a radioactive source.
Rutherford found that when alpha particles passed through nitrogen gas, fast-moving particles were produced. These particles were identified as protons. The residual nucleus was identified as oxygen-17.
\[ {}^{14}_{7}\mathrm{N}+{}^{4}_{2}\mathrm{He} \rightarrow {}^{17}_{8}\mathrm{O}+{}^{1}_{1}\mathrm{H} \]
Thus, nitrogen was transformed into oxygen:
\[ {}^{14}_{7}\mathrm{N} \longrightarrow {}^{17}_{8}\mathrm{O} \]
Since the atomic number changes from \(7\) to \(8\), the element changes from nitrogen to oxygen. This demonstrated that one element could be artificially transformed into another element through a nuclear reaction.
Rutherford’s Experimental Arrangement
In Rutherford’s experiment, a radioactive source produced alpha particles. The alpha particles were directed into a chamber containing nitrogen gas. When the alpha particles interacted with nitrogen nuclei, a nuclear reaction occurred. The resulting fast protons were detected using a scintillation screen or suitable particle-detection arrangement.
Symbolic Representation of the Experiment
The experimental arrangement shown above can be represented symbolically as
\[ \boxed{ {}^{14}_{7}\mathrm{N} + {}^{4}_{2}\mathrm{He} \rightarrow {}^{17}_{8}\mathrm{O} + {}^{1}_{1}\mathrm{H} } \]
The symbols in the reaction represent the following:
| Symbol | Meaning |
|---|---|
| \( {}^{14}_{7}\mathrm{N} \) | Nitrogen-14 target nucleus |
| \( {}^{4}_{2}\mathrm{He} \) | Alpha particle used to bombard the target nucleus |
| \( {}^{17}_{8}\mathrm{O} \) | Oxygen-17 product nucleus |
| \( {}^{1}_{1}\mathrm{H} \) | Hydrogen-1 nucleus, which is a proton |
Verification of Conservation Laws
The Rutherford transmutation reaction satisfies the conservation of nucleon number.
\[ 14+4=17+1 \]
Therefore, the total number of nucleons is \(18\) on both sides.
It also satisfies the conservation of electric charge:
\[ 7+2=8+1 \]
Therefore, the total nuclear charge is \(+9e\) before and after the reaction.
Importance of Artificial Transmutation
Artificial transmutation demonstrated that the nucleus of an element can be deliberately transformed into the nucleus of another element. It provided important evidence for the nuclear nature of matter and opened the way for the development of artificial nuclear reactions, radioisotopes, nuclear reactors, and nuclear physics.
Artificial transmutation is also important because suitable nuclear reactions can be used to produce radioactive isotopes that are useful in medicine, industry, agriculture, and scientific research.
Thus, artificial transmutation is the deliberate transformation of one element into another by inducing a nuclear reaction with a suitable incident particle.
Discovery of Neutron
The neutron is a neutral subatomic particle present in the nucleus of an atom. It has no electric charge and its mass is nearly equal to that of a proton.
The existence of a neutral particle in the nucleus was proposed to explain why the mass of an atomic nucleus could not be accounted for by protons alone. The neutron was discovered experimentally by James Chadwick in 1932.
Chadwick’s Experiment
Chadwick bombarded a thin sample of beryllium with alpha particles obtained from a radioactive source. A highly penetrating radiation was produced from the beryllium. This radiation was electrically neutral and was therefore not deflected by electric or magnetic fields.
Chadwick allowed this radiation to fall on substances containing light nuclei, particularly paraffin wax. The radiation caused fast-moving protons to be ejected from the paraffin wax. The high energy of these protons could not be explained satisfactorily if the radiation consisted of gamma rays.
Chadwick concluded that the radiation consisted of a new type of neutral particle having a mass approximately equal to the mass of a proton. He called this particle the neutron.
Nuclear Reaction Responsible for the Production of Neutrons
When beryllium is bombarded with alpha particles, a neutron is emitted and carbon-12 is produced.
\[ {}^{9}_{4}\mathrm{Be} + {}^{4}_{2}\mathrm{He} \rightarrow {}^{12}_{6}\mathrm{C} + {}^{1}_{0}\mathrm{n} \]
In this reaction, the alpha particle interacts with the beryllium-9 nucleus. The resulting nucleus is carbon-12 and a neutron is emitted.
The conservation of mass number can be verified as
\[ 9+4=12+1 \]
The conservation of atomic number can also be verified:
\[ 4+2=6+0 \]
Thus, both nucleon number and electric charge are conserved in the reaction.
Chadwick’s Experimental Arrangement
The essential arrangement used by Chadwick is shown below. Alpha particles from a radioactive source were directed onto a beryllium target. The resulting neutral radiation then entered a chamber containing paraffin wax. The neutral particles knocked protons out of the hydrogen-rich paraffin wax, and the recoiling protons were detected and studied.
Explanation of the Experimental Arrangement
1. Alpha-particle source: A radioactive source was used to provide energetic alpha particles.
2. Beryllium target: The alpha particles were directed onto a beryllium target. The nuclear reaction produced a highly penetrating neutral radiation.
3. Neutral radiation: The radiation emerging from the beryllium was not deflected by electric or magnetic fields, indicating that it carried no electric charge.
4. Paraffin wax: The neutral radiation was allowed to fall on paraffin wax, which contains a large number of hydrogen nuclei.
5. Recoil protons: The neutral radiation caused high-speed protons to be ejected from the hydrogen nuclei in the paraffin wax.
6. Detection: The recoiling protons were detected and their energies were measured. From these observations, Chadwick established that the incident neutral particles had a mass comparable to that of a proton.
Why Chadwick Concluded That the Radiation Was Neutron Radiation
The observed radiation was highly penetrating and was not deflected by electric or magnetic fields. Therefore, it had no electric charge. However, it was capable of transferring a large amount of energy and momentum to light nuclei such as hydrogen nuclei.
If the radiation had consisted of gamma-ray photons, the observed energies of the recoil protons could not be satisfactorily explained. Chadwick showed that the observations were consistent with a neutral particle having a mass approximately equal to the mass of a proton.
This particle was named the neutron and was represented by the symbol
\[ {}^{1}_{0}\mathrm{n} \]
The mass number of a neutron is \(1\), while its atomic number is \(0\), indicating that it is electrically neutral.
Properties of Neutrons
1. Neutrons are electrically neutral particles. Their electric charge is zero.
\[ q_n=0 \]
2. A neutron is represented by \( {}^{1}_{0}\mathrm{n} \). Its mass number is \(1\) and its atomic number is \(0\).
3. The mass of a neutron is approximately equal to the mass of a proton. The neutron is slightly heavier than the proton.
\[ m_n \approx 1.675\times10^{-27}\ \mathrm{kg} \]
4. Neutrons are constituents of most atomic nuclei. They combine with protons to form the nucleus of an atom. The nucleus of ordinary hydrogen-1 is an important exception because it contains only one proton.
5. Neutrons are not deflected by electric fields. Since they have no electric charge, an electric field does not exert an electric force on a free neutron.
6. Neutrons are not deflected by magnetic fields in the same way as charged particles. They have no net electric charge, although the neutron has an intrinsic magnetic moment because of its internal structure.
7. Free neutrons are unstable. A free neutron outside an atomic nucleus undergoes beta decay with a mean lifetime of about \(15\) minutes.
\[ {}^{1}_{0}\mathrm{n} \rightarrow {}^{1}_{1}\mathrm{p} + {}^{0}_{-1}\mathrm{e} + \bar{\nu}_e \]
8. Neutrons are highly penetrating particles. Since they carry no electric charge, they do not lose energy through direct Coulomb interactions with electrons in the same way as charged particles. Their interactions with nuclei therefore play an important role in neutron shielding and nuclear reactions.
9. Neutrons play an important role in nuclear reactions. Because they have no electric charge, neutrons can enter many atomic nuclei without experiencing electrostatic repulsion from the positively charged nucleus.
10. Neutrons are important in nuclear fission and nuclear reactors. A neutron can initiate the fission of suitable heavy nuclei such as uranium-235, releasing energy and additional neutrons that can participate in further fission reactions.
Thus, the discovery of the neutron completed the basic picture of the atomic nucleus as a system consisting primarily of protons and neutrons and provided the foundation for much of modern nuclear physics.
Radio Isotopes
Radioisotopes are isotopes of an element whose nuclei are unstable and undergo spontaneous radioactive decay by emitting α-particles, β-particles, γ-rays, or other nuclear radiation.
Isotopes are atoms of the same element having the same atomic number but different mass numbers. Therefore, all isotopes of an element have the same number of protons but different numbers of neutrons. Some isotopes are stable, whereas others are unstable and undergo radioactive decay. The unstable isotopes are called radioisotopes.
Characteristics of Radioisotopes
A radioisotope has an unstable nucleus. It spontaneously changes into a more stable nucleus by emitting radiation. The process is not significantly affected by ordinary physical conditions such as temperature, pressure, or chemical state.
The radioactive decay of a radioisotope is governed by the radioactive decay law:
\[ N=N_0e^{-\lambda t} \]
where \(N_0\) is the initial number of radioactive nuclei, \(N\) is the number of undecayed nuclei after time \(t\), and \(\lambda\) is the decay constant of the radioisotope.
The activity of a radioactive sample is given by
\[ A=\lambda N \]
Thus, the activity decreases continuously as the number of undecayed nuclei decreases.
Examples of Radioisotopes
Several radioisotopes occur naturally, while many others are produced artificially in nuclear reactions. Some important examples are carbon-14, cobalt-60, iodine-131, phosphorus-32, and technetium-99m.
| Radioisotope | Symbolic representation | Type |
|---|---|---|
| Carbon-14 | \( {}^{14}_{6}\mathrm{C} \) | Naturally occurring |
| Cobalt-60 | \( {}^{60}_{27}\mathrm{Co} \) | Artificially produced |
| Iodine-131 | \( {}^{131}_{53}\mathrm{I} \) | Artificially produced |
| Phosphorus-32 | \( {}^{32}_{15}\mathrm{P} \) | Artificially produced |
| Technetium-99m | \( {}^{99m}_{43}\mathrm{Tc} \) | Artificially produced |
Natural and Artificial Radioisotopes
Natural radioisotopes are radioactive isotopes that occur naturally in the environment. Examples include carbon-14, potassium-40, and uranium-238.
Artificial radioisotopes are radioactive isotopes produced intentionally by nuclear reactions. They can be produced by bombarding stable nuclei with suitable particles in nuclear reactors or particle accelerators.
For example, phosphorus-32 can be produced by neutron bombardment of phosphorus-31:
\[ {}^{31}_{15}\mathrm{P} + {}^{1}_{0}\mathrm{n} \rightarrow {}^{32}_{15}\mathrm{P} + \gamma \]
In this reaction, phosphorus-31 captures a neutron and becomes the radioactive isotope phosphorus-32. The emitted gamma radiation carries away excess energy.
Radioactive Decay of a Radioisotope
The nucleus of a radioisotope may undergo alpha decay, beta decay, or gamma decay depending on its nuclear structure. During radioactive decay, the original radioisotope is transformed into another nucleus.
For example, carbon-14 undergoes beta decay to form nitrogen-14:
\[ {}^{14}_{6}\mathrm{C} \rightarrow {}^{14}_{7}\mathrm{N} + {}^{0}_{-1}\mathrm{e} + \bar{\nu}_e \]
Here, the mass number remains \(14\), while the atomic number increases from \(6\) to \(7\). The emitted electron is the beta particle.
Half-Life of Radioisotopes
The half-life of a radioisotope is the time required for half of the radioactive nuclei initially present in a sample to undergo decay.
\[ T_{1/2}=\frac{\ln 2}{\lambda} \]
\[ T_{1/2}=\frac{0.693}{\lambda} \]
Different radioisotopes have different half-lives. Some decay within fractions of a second, whereas others have half-lives extending to thousands or millions of years. The half-life is a characteristic property of a particular radioactive nuclide.
Radioisotopes as Tracers
Because radioisotopes emit detectable radiation, a small quantity of a suitable radioisotope can be introduced into a system and its movement can be followed using radiation detectors. Such a radioisotope is called a radioactive tracer.
The tracer technique allows scientists and medical professionals to study the movement or distribution of a substance without significantly altering the system being investigated. The specific applications of radioisotopes and radioactive tracers are discussed in the next subtopic, Uses of Radioisotopes.
Thus, radioisotopes are unstable isotopes that undergo spontaneous nuclear decay and emit radiation. Their predictable radioactive properties make them valuable tools in science, medicine, industry, agriculture, and research.
Uses of Radioisotopes
The presence, location, and quantity of a radioactive isotope in a particular system can be determined by detecting the radiation emitted by it. Because radioactive emissions can be detected and measured with high sensitivity, radioisotopes are widely used as tracers and sources of radiation in chemistry, agriculture, medicine, industry, and geology.
A few important applications of radioisotopes are described below.
1. Chemistry
a) Chemical Analysis: Radioisotopes are used to determine the solubility of sparingly soluble salts such as lead sulphate (\(\mathrm{PbSO_4}\)) and silver chloride (\(\mathrm{AgCl}\)). They are also used for determining trace quantities of elements present in industrial raw materials and products.
b) Study of Reaction Mechanisms: Radioisotopes can be used as tracers to investigate chemical reaction mechanisms. For example, the oxygen isotope \(^{18}_{8}\mathrm{O}\) can be used to study the mechanisms of photosynthesis and the hydrolysis of esters.
2. Agriculture
a) Study of Phosphorus Absorption: The radioisotope phosphorus-32, \(^{32}_{15}\mathrm{P}\), is used to study the absorption of phosphorus by plants.
b) Study of Mineral Transport: The radioisotope sulphur-34, \(^{34}_{16}\mathrm{S}\), can be used as a tracer to study the transport of sulphur and other minerals in plants.
c) Improvement of Crop Yield: Controlled irradiation of seeds using suitable gamma radiation can be used in plant-breeding research to produce useful variations and develop improved crop varieties.
3. Medical Field
Radioisotopes have important applications in medical diagnosis, medical imaging, functional studies, and radiation treatment.
a) Diagnosis and Treatment of Certain Tumours: Radioisotopes such as iodine-131, \(^{131}_{53}\mathrm{I}\), can be used in the diagnosis and treatment of certain thyroid-related conditions and cancers.
b) Study of Blood Circulation: Suitable radioactive tracers can be used to study blood circulation and to detect restricted or abnormal blood flow.
c) Study of Heart Function: Radioactive tracers can be used in nuclear-medicine investigations to study the pumping and functioning of the heart.
d) Study of the Thyroid Gland: Iodine-131, \(^{131}_{53}\mathrm{I}\), is taken up by the thyroid gland and can therefore be used to study its functioning. It is also used therapeutically in selected thyroid disorders.
e) Detection and Treatment of Cancer: Cobalt-60, \(^{60}_{27}\mathrm{Co}\), is a source of penetrating gamma radiation and has been used in radiation therapy for the treatment of cancer.
f) Treatment of Certain Blood Disorders: Phosphorus-32, \(^{32}_{15}\mathrm{P}\), has been used in the treatment of certain blood disorders under appropriate medical supervision.
g) Treatment of Thyroid Disorders: Iodine-131, \(^{131}_{53}\mathrm{I}\), is used in the treatment of certain thyroid disorders because the thyroid naturally concentrates iodine.
4. Industry
a) Selection of Appropriate Lubricants: Radioisotopic tracer techniques can be used to study the behaviour and wear of lubricants in machinery and thereby help in selecting suitable lubricants.
b) Detection of Flaws in Machines: Radioactive radiation is used in non-destructive testing to detect internal defects, cracks, voids, and other flaws in machine components and industrial structures without destroying them.
5. Geology
a) Determination of the Age of Fossils: The radioisotope carbon-14, \(^{14}_{6}\mathrm{C}\), is used in radiocarbon dating to estimate the age of suitable once-living materials and archaeological remains.
b) Determination of the Age of Rocks: The age of rocks can be determined using radioactive decay systems. For example, the uranium-lead dating method uses the decay of \(^{238}_{92}\mathrm{U}\) to \(^{206}_{82}\mathrm{Pb}\).
\[ {}^{238}_{92}\mathrm{U} \longrightarrow {}^{206}_{82}\mathrm{Pb} +\text{decay products} \]
The measured ratio of the parent isotope \(^{238}_{92}\mathrm{U}\) to the radiogenic daughter product \(^{206}_{82}\mathrm{Pb}\), together with the known radioactive decay characteristics, provides information about the age of the rock.
Thus, radioisotopes serve as powerful tools for tracing substances, studying chemical and biological processes, diagnosing and treating diseases, testing industrial materials, and determining the ages of geological and archaeological materials.
Nuclear Fission
Nuclear fission is the process in which a heavy atomic nucleus splits into two or more lighter nuclei of comparable mass, along with the emission of neutrons and a large amount of energy.
The fission process usually occurs when a heavy nucleus such as uranium-235, uranium-233, or plutonium-239 absorbs a neutron and becomes highly excited. The excited nucleus becomes unstable and deforms, eventually splitting into two lighter nuclei called fission fragments. Additional neutrons and a large amount of energy are also released.
Discovery of Nuclear Fission
Nuclear fission was discovered in 1938 through the experiments of Otto Hahn and Fritz Strassmann. They bombarded uranium with neutrons and found evidence of much lighter elements, particularly barium, among the products.
The result was unexpected because uranium is a very heavy nucleus, whereas barium is much lighter. Lise Meitner and Otto Frisch explained the experimental result in 1939 and recognized that the uranium nucleus had split into two smaller nuclei. Frisch introduced the term nuclear fission for this process.
Theory of Nuclear Fission
The liquid-drop model of the nucleus provides a useful qualitative explanation of nuclear fission. A heavy nucleus behaves in some respects like a charged liquid drop. Two competing effects are important: the strong nuclear force tends to hold the nucleus together, while the electrostatic repulsion between the positively charged protons tends to separate the nucleus.
When a heavy nucleus absorbs a neutron, it may form an excited compound nucleus. The extra energy can cause the nucleus to deform from its nearly spherical shape into an elongated shape. If the deformation becomes sufficiently large, the attractive nuclear force can no longer overcome the increasing electrostatic repulsion between the two parts of the nucleus.
The elongated nucleus develops a constriction, or neck, and finally separates into two fragments. The two positively charged fragments repel each other strongly and move apart with high kinetic energy.
\[ \text{Heavy nucleus} \rightarrow \text{Excited nucleus} \rightarrow \text{Deformed nucleus} \rightarrow \text{Two fission fragments} \]
Fission of Uranium-235
A typical example of neutron-induced fission is the fission of uranium-235. When a slow neutron is absorbed by a uranium-235 nucleus, an excited uranium-236 nucleus is formed:
\[ {}^{235}_{92}\mathrm{U} + {}^{1}_{0}\mathrm{n} \rightarrow {}^{236}_{92}\mathrm{U}^{*} \]
The excited uranium-236 nucleus can then undergo fission. One possible fission channel is
\[ {}^{236}_{92}\mathrm{U}^{*} \rightarrow {}^{141}_{56}\mathrm{Ba} + {}^{92}_{36}\mathrm{Kr} + 3\,{}^{1}_{0}\mathrm{n} + Q \]
The mass numbers are conserved:
\[ 236=141+92+3 \]
The atomic numbers are also conserved:
\[ 92=56+36 \]
The above is only one possible fission channel. A uranium-235 nucleus can undergo fission in several different ways, producing different pairs of fission fragments and different numbers of neutrons.
Fission of Different Heavy Elements
Nuclear fission is not restricted to uranium-235. Several heavy nuclei can undergo fission when supplied with suitable excitation energy. Important fissile nuclides include uranium-233, uranium-235, and plutonium-239.
For example, uranium-233 can undergo neutron-induced fission:
\[ {}^{233}_{92}\mathrm{U} + {}^{1}_{0}\mathrm{n} \rightarrow {}^{234}_{92}\mathrm{U}^{*} \rightarrow \text{fission fragments} + \text{neutrons} + \text{energy} \]
Similarly, plutonium-239 can undergo neutron-induced fission:
\[ {}^{239}_{94}\mathrm{Pu} + {}^{1}_{0}\mathrm{n} \rightarrow {}^{240}_{94}\mathrm{Pu}^{*} \rightarrow \text{fission fragments} + \text{neutrons} + \text{energy} \]
The exact fission fragments are not unique. A particular fissile nucleus can split through many different channels, provided that the conservation laws are satisfied.
Fission with Different Projectiles
Nuclear fission can be induced by supplying sufficient energy to a heavy nucleus. Neutrons are especially important because they have no electric charge and therefore do not experience electrostatic repulsion from the positively charged nucleus.
Heavy nuclei can also be excited by other projectiles such as protons, alpha particles, deuterons, and other nuclei when they have sufficient energy. Such projectiles must overcome the electrostatic repulsion between the positively charged projectile and the target nucleus.
Thus, the probability and nature of fission depend on the target nucleus, the type and energy of the projectile, and the excitation energy produced in the compound nucleus.
\[ \text{Target nucleus} + \text{projectile} \rightarrow \text{excited compound nucleus} \rightarrow \text{fission fragments} + \text{neutrons} + \text{energy} \]
Fission Products
The two lighter nuclei produced when a heavy nucleus undergoes fission are called fission fragments or fission products.
The fission fragments are generally radioactive because they contain an excess of neutrons compared with stable nuclei of similar mass. They therefore undergo further radioactive transformations, mainly beta decay, until more stable nuclei are formed.
For example, one possible fission reaction is
\[ {}^{235}_{92}\mathrm{U} + {}^{1}_{0}\mathrm{n} \rightarrow {}^{141}_{56}\mathrm{Ba} + {}^{92}_{36}\mathrm{Kr} + 3\,{}^{1}_{0}\mathrm{n} + Q \]
Here, \(^{141}_{56}\mathrm{Ba}\) and \(^{92}_{36}\mathrm{Kr}\) are the fission fragments, while the three neutrons can participate in subsequent nuclear reactions.
Energy Liberated in Nuclear Fission
A large amount of energy is released during nuclear fission because the total mass of the fission products is slightly less than the mass of the original nucleus together with the incident neutron.
The mass difference is converted into energy according to Einstein’s mass-energy relation:
\[ E=\Delta mc^2 \]
For a typical fission of uranium-235, the energy released is approximately 200 MeV per fission event. Most of this energy appears as the kinetic energy of the two fission fragments. Smaller amounts are carried by the emitted neutrons and gamma radiation, and some energy is subsequently released through the radioactive decay of the fission products.
\[ 200\ \mathrm{MeV} \approx 3.2\times10^{-11}\ \mathrm{J} \]
Although the energy released by one fission event is extremely small on an ordinary scale, an enormous number of nuclei undergo fission in a macroscopic sample. Consequently, the total energy released can be very large.
Production of Neutrons in Nuclear Fission
One of the most important features of nuclear fission is the emission of additional neutrons. In the fission of uranium-235 induced by a neutron, typically two or three neutrons are released, although the exact number varies from one fission event to another.
\[ {}^{235}_{92}\mathrm{U} + {}^{1}_{0}\mathrm{n} \rightarrow {}^{236}_{92}\mathrm{U}^{*} \rightarrow \text{fission fragments} + 2\text{ or }3\,{}^{1}_{0}\mathrm{n} + \text{energy} \]
The emitted neutrons can strike other fissile nuclei and cause them to undergo fission. Therefore, one fission event can lead to further fission events. This process is known as a chain reaction, which is discussed in the next topic.
The production of neutrons is therefore essential for sustaining a nuclear chain reaction. Whether the released neutrons produce further fissions depends on factors such as the type of fuel, neutron energy, geometry of the material, and the presence of neutron absorbers.
Thus, nuclear fission is the splitting of a heavy nucleus into lighter nuclei with the release of neutrons and a large amount of energy. The released neutrons make it possible for successive fission events to occur, forming the basis of a nuclear chain reaction.
Chain Reaction
A nuclear chain reaction is a self-sustaining sequence of nuclear reactions in which neutrons released in one fission reaction cause further fission reactions, producing additional neutrons that can initiate still more fissions.
In the fission of a heavy nucleus such as uranium-235, two or three neutrons are generally released along with the fission fragments and a large amount of energy. If these neutrons are able to cause fission in other fissile nuclei, the newly produced neutrons can cause further fissions. Thus, a sequence of successive fission reactions is established.
Principle of Nuclear Chain Reaction
The basic principle of a chain reaction is the multiplication of neutrons through successive fission events. A simplified sequence can be represented as
\[ \text{One fission} \rightarrow \text{more neutrons} \rightarrow \text{more fissions} \rightarrow \text{still more neutrons} \rightarrow \text{successive fissions} \]
For example, a neutron can initiate the fission of uranium-235:
\[ {}^{235}_{92}\mathrm{U} + {}^{1}_{0}\mathrm{n} \rightarrow \text{fission fragments} + 2\text{ or }3\,{}^{1}_{0}\mathrm{n} + \text{energy} \]
The neutrons released in this fission can interact with other uranium-235 nuclei and produce further fission events.
Diagrammatic Representation of a Chain Reaction
The following schematic representation shows how one generation of neutrons can produce the next generation of fissions. The diagram is not drawn to scale; it is intended to show the multiplication process clearly.
Neutron Multiplication Factor
The neutron multiplication factor \(K\) is the ratio of the number of neutrons in one generation that are capable of producing further fissions to the corresponding number of neutrons in the preceding generation.
\[ K= \frac{\text{Number of neutrons in one generation}} {\text{Number of neutrons in the preceding generation}} \]
The value of \(K\) determines whether the chain reaction decreases, remains steady, or increases.
Cases of Neutron Multiplication Factor
1. Subcritical condition: \(K<1\)
When \(K<1\), fewer neutrons are available in each successive generation to cause further fissions. The chain reaction gradually decreases and eventually stops.
2. Critical condition: \(K=1\)
When \(K=1\), each generation produces, on average, the same number of effective neutrons as the preceding generation. The chain reaction becomes self-sustaining and the rate of fission remains approximately constant.
3. Supercritical condition: \(K>1\)
When \(K>1\), the number of effective neutrons increases from one generation to the next. Consequently, the number of fission events increases rapidly.
| Condition | Value of \(K\) | Behaviour of chain reaction |
|---|---|---|
| Subcritical | \(K<1\) | Reaction decreases and stops |
| Critical | \(K=1\) | Self-sustaining reaction |
| Supercritical | \(K>1\) | Reaction increases |
Conditions for a Sustained Chain Reaction
A sustained chain reaction requires conditions under which, on average, at least one neutron from each generation produces a further fission in the next generation. In terms of the multiplication factor, the ideal condition for a steady sustained chain reaction is
\[ K=1 \]
The important physical requirements include the following:
1. Suitable fissile material: A sufficient quantity of a suitable fissile nuclide must be present so that neutrons have a reasonable probability of causing further fissions.
2. Adequate neutron economy: Enough of the neutrons produced by fission must remain available to cause further fissions. Neutron leakage and unwanted neutron absorption must be controlled.
3. Appropriate neutron energy: The energy of the neutrons must be suitable for the particular fissile material. In some reactor systems, moderators are used to reduce neutron energy and increase the probability of further fission.
4. Suitable arrangement of the fissile material: The physical arrangement and size of the fuel affect neutron leakage and therefore affect the multiplication factor.
5. Control of neutron absorption: Materials that absorb neutrons without producing fission can reduce the multiplication factor. In a reactor, controlled neutron absorption is used to regulate the chain reaction.
Chain Reaction in a Nuclear Reactor
A nuclear reactor is designed to maintain a controlled and approximately steady nuclear chain reaction. The energy released by fission is converted into useful heat, which can ultimately be used to generate electricity.
In a typical reactor, the fuel contains fissile material. Neutrons produced by fission cause further fissions. A moderator, where required, slows down fast neutrons, while control rods absorb neutrons and regulate the multiplication factor.
The reactor is normally operated so that the effective multiplication factor is maintained close to
\[ K\approx1 \]
This allows the fission rate and power output to be controlled rather than increasing without limit. The detailed principle and working of a nuclear reactor will be discussed in the next topic.
Chain Reaction and Nuclear Weapons
A rapidly increasing fission chain reaction is also the physical principle underlying a fission nuclear weapon. In such a context, the chain reaction is allowed to become strongly supercritical for a very short period, causing an extremely rapid release of nuclear energy.
This is fundamentally different from the operation of a nuclear reactor. A reactor is engineered to control the chain reaction and remove the released heat continuously, whereas a nuclear weapon is designed around an extremely rapid, uncontrolled release of fission energy.
The detailed design, dimensions, material arrangements, or procedures used to construct a nuclear weapon are not part of this topic. For understanding nuclear physics, the essential distinction is the behaviour of the neutron multiplication factor:
\[ \boxed{ \begin{array}{c} K<1 \quad\rightarrow\quad \text{chain reaction decreases}\\[4pt] K=1 \quad\rightarrow\quad \text{controlled/self-sustaining condition}\\[4pt] K>1 \quad\rightarrow\quad \text{chain reaction increases} \end{array}} \]
Thus, a nuclear chain reaction is a sequence of successive fission reactions maintained by the neutrons produced during fission. The neutron multiplication factor \(K\) determines the behaviour of the chain reaction, while controlled neutron production and absorption make sustained operation possible in a nuclear reactor.
Principle and Working of a Nuclear Reactor
Principle of a Nuclear Reactor
A nuclear reactor works on the principle of a controlled and sustained nuclear chain reaction in which the energy released during nuclear fission is converted into useful heat energy.
In a typical nuclear reactor, the fission of a suitable heavy nucleus such as uranium-235 is initiated by neutrons. Each fission event releases a large amount of energy and additional neutrons. These neutrons can produce further fission reactions, thereby establishing a chain reaction.
The chain reaction is carefully controlled so that the reactor operates at an approximately constant rate. The heat produced by the fission reactions is transferred to a coolant. The coolant carries this heat to a steam generator or directly to a steam-producing system, depending on the type of reactor. The steam then drives a turbine connected to an electric generator.
\[ \boxed{ \text{Nuclear energy} \rightarrow \text{Heat energy} \rightarrow \text{Mechanical energy} \rightarrow \text{Electrical energy} } \]
Working of a Nuclear Reactor
The working of a nuclear reactor can be understood by following the successive stages from nuclear fission to the generation of electrical energy.
Schematic Diagram of a Nuclear Reactor
The following diagram shows the basic arrangement of a nuclear power reactor. The exact arrangement varies with reactor design, but the essential functions of fuel, moderator, control rods, coolant, heat transfer, turbine, generator, condenser, and shielding are represented.
Description of the Nuclear Reactor
A nuclear reactor consists of a collection of components arranged to initiate, control, sustain, and safely extract energy from a nuclear chain reaction. The central region in which fission occurs is called the reactor core.
The main components and their functions are described below.
1. Nuclear Fuel
Nuclear fuel is the fissile material that undergoes nuclear fission and releases energy. Common reactor fuels include uranium-235, uranium-233, and plutonium-239, depending on the reactor design.
\[ {}^{235}_{92}\mathrm{U} + {}^{1}_{0}\mathrm{n} \rightarrow \text{Fission products} + 2\text{ or }3\,{}^{1}_{0}\mathrm{n} + \text{Energy} \]
The fuel is generally formed into fuel pellets or other suitable fuel elements and arranged inside the reactor core.
2. Reactor Core
The reactor core is the central region of the reactor in which the nuclear fission reactions take place. It contains the fuel together with the moderator, control elements, and coolant passages, depending on the reactor design.
The energy released by fission in the core appears primarily as kinetic energy of the fission fragments. This energy is rapidly converted into thermal energy within the fuel and surrounding material.
3. Moderator
A moderator is a material used in many reactors to slow down fast neutrons produced during fission. Common moderators include ordinary water, heavy water, and graphite.
The purpose of slowing the neutrons is to increase the probability of further fission in reactor fuels for which slow-neutron fission is more probable, such as uranium-235.
\[ \text{Fast neutron} \rightarrow \text{moderator} \rightarrow \text{slower neutron} \]
4. Control Rods
Control rods are neutron-absorbing materials used to regulate the rate of the nuclear chain reaction. Materials such as boron, cadmium, and hafnium are used in various reactor designs.
When the control rods are inserted further into the reactor core, they absorb more neutrons and reduce the number of neutrons available to cause further fission. When they are withdrawn appropriately, fewer neutrons are absorbed and the fission rate can increase.
\[ \text{More control-rod insertion} \rightarrow \text{more neutron absorption} \rightarrow \text{lower fission rate} \]
5. Coolant
The coolant removes the heat produced in the reactor core and transfers it to another part of the power-generation system.
Depending on the reactor design, water, heavy water, carbon dioxide, helium, or certain liquid metals can be used as coolants.
\[ \text{Fission heat} \rightarrow \text{coolant} \rightarrow \text{steam generator} \]
6. Reactor Vessel
The reactor vessel is a strong pressure-containing structure that encloses the reactor core and the associated coolant under the required operating conditions.
It is designed to withstand high temperature, pressure, and radiation and to maintain the reactor coolant within the primary system.
7. Steam Generator
In reactor systems that use a separate steam generator, the heat carried by the primary coolant is transferred to water in a secondary system. The secondary water is converted into steam.
\[ \text{Hot coolant} \rightarrow \text{heat exchanger} \rightarrow \text{water} \rightarrow \text{steam} \]
The primary coolant and the secondary water can be kept in separate circuits so that heat is transferred without necessarily mixing the two fluids.
8. Turbine
The turbine converts the energy of high-pressure steam into mechanical rotational energy.
When steam passes over the turbine blades, it causes the turbine shaft to rotate. The rotating shaft is mechanically coupled to an electrical generator.
9. Generator
The generator converts the mechanical energy of the rotating turbine into electrical energy.
\[ \text{Mechanical energy} \rightarrow \text{Electrical energy} \]
10. Condenser
The condenser converts the exhaust steam from the turbine back into liquid water.
The condensed water can then be pumped back toward the steam-generating system. This allows the water-steam cycle to operate continuously.
11. Cooling System
The cooling system removes waste heat from the condenser. Depending on the plant design, cooling may be provided using a cooling tower, a water body, or another heat-rejection system.
12. Biological Shielding
Biological shielding is a thick layer of suitable material surrounding radiation-producing parts of the reactor to reduce radiation exposure to workers and the surrounding environment.
Concrete, steel, water, and other shielding materials may be used in different parts of a nuclear facility depending on the type and energy of the radiation that must be attenuated.
Stages Involved in the Working of a Nuclear Reactor
Stage 1 – Initiation and control of fission: Neutrons interact with fissile nuclei in the reactor core and initiate nuclear fission. A controlled chain reaction is maintained.
\[ \text{Fissile nucleus} + \text{neutron} \rightarrow \text{fission products} + \text{neutrons} + \text{energy} \]
Stage 2 – Production of heat: The kinetic energy of the fission fragments and other reaction products is converted into thermal energy in the reactor core.
Stage 3 – Heat removal: The coolant flows through or around the reactor core and carries the heat away from the fuel.
Stage 4 – Production of steam: The heat is transferred to water in a steam-generating system, producing high-pressure steam in reactor designs that use a secondary steam cycle.
Stage 5 – Rotation of the turbine: The high-pressure steam expands through the turbine and converts its thermal energy into mechanical rotational energy.
Stage 6 – Generation of electricity: The rotating turbine drives the generator, which produces electrical energy.
Stage 7 – Condensation and recycling: The exhaust steam is cooled in the condenser and converted back into water. The water is pumped back into the steam-generating system.
\[ \boxed{ \text{Fission} \rightarrow \text{Heat} \rightarrow \text{Steam} \rightarrow \text{Turbine} \rightarrow \text{Generator} \rightarrow \text{Electricity} } \]
Role of the Nuclear Reactor in Power Generation
The nuclear reactor acts as the heat source of a nuclear power plant. Unlike a conventional thermal power plant, where heat is obtained by burning a fuel, a nuclear power plant obtains heat from nuclear fission.
The reactor itself does not directly produce electricity. Its primary function is to release and control nuclear energy and transfer the resulting heat to the power-conversion system.
\[ \text{Nuclear fuel} \rightarrow \text{Nuclear fission} \rightarrow \text{Heat} \rightarrow \text{Steam} \rightarrow \text{Turbine} \rightarrow \text{Generator} \rightarrow \text{Electricity} \]
Thus, a nuclear reactor is a carefully engineered system in which a controlled nuclear chain reaction produces heat, the heat is transferred by a coolant, and the resulting thermal energy is converted through a turbine-generator system into useful electrical energy.
Nuclear Radiation Hazards
Nuclear radiations are high-energy radiations emitted from unstable atomic nuclei during radioactive decay or nuclear reactions. The important nuclear radiations include α-particles, β-particles, γ-rays, neutrons and other high-energy particles.
The intensity of nuclear radiation represents the amount of radiation received or the rate at which radiation energy is delivered to a given area or material. Its biological effect depends not only on the intensity but also on the type of radiation, exposure time, and the sensitivity of the tissue.
When nuclear radiation passes through living tissue, it can ionise atoms and molecules and break important chemical bonds. This may damage cells, particularly the DNA and other molecules essential for normal cell function.
Radiation damage may cause cell death, tissue injury, impaired organ function and, after sufficiently large or repeated exposures, an increased risk of diseases such as cancer.
Genetic damage occurs when radiation causes changes in the DNA present in cells. If the damage occurs in reproductive cells and is not correctly repaired, it may be transmitted to the next generation.
Mutations are permanent changes in the genetic material of a cell. Radiation-induced mutations may arise from changes in the DNA sequence or from larger alterations in chromosomes. Such mutations may have harmful effects, although not every mutation produces an observable effect.
The severity of radiation damage depends on factors such as radiation dose, dose rate, type and energy of radiation, duration of exposure, part of the body exposed and the sensitivity of the particular tissue.
Therefore, unnecessary exposure to nuclear radiation must be avoided, and appropriate protective measures and shielding must be used wherever radioactive materials or radiation-producing equipment are handled.
Protective Shielding
Protective shielding is the use of suitable materials placed between a source of nuclear radiation and a person or sensitive equipment to reduce the intensity of radiation reaching them.
The choice of shielding material depends on the type, energy and intensity of radiation. The main aim is to absorb or attenuate radiation sufficiently to keep the exposure within safe limits.
Alpha radiation has very low penetrating power and can be stopped by a sheet of paper, the outer dead layer of skin, or a few centimetres of air. Therefore, external shielding against alpha particles is generally simple.
Beta radiation has greater penetrating power than alpha radiation. Materials such as plastic, acrylic or aluminium are commonly used for shielding beta particles. High-Z materials are generally avoided as the first shielding layer because they can produce bremsstrahlung X-rays.
Gamma rays have very high penetrating power and require dense materials for effective shielding. Lead, steel and concrete are commonly used, with the required thickness depending on the photon energy and desired reduction in intensity.
Neutrons are electrically neutral and require different shielding materials. Hydrogen-rich materials such as water, polyethylene and concrete are useful for slowing fast neutrons, while additional neutron-absorbing materials may be used to capture them.
The effectiveness of shielding increases with its thickness. In general, increasing the distance from the radiation source, reducing the exposure time, and using appropriate shielding are the three fundamental methods of reducing radiation exposure.
Thus, proper shielding, minimum exposure time and maximum practical distance from the radiation source are essential for radiation protection.
Types of Nuclear Reactors
Nuclear reactors are devices in which a controlled and sustained nuclear chain reaction is used to produce useful energy. Depending on their purpose, nuclear reactors are broadly classified into breeder reactors and power reactors.
Breeder Reactors: A breeder reactor is a nuclear reactor designed to produce more fissile material than it consumes. It converts fertile nuclei such as uranium-238 into fissile plutonium-239 while producing energy through nuclear fission.
In a uranium-based breeder reactor, uranium-238 absorbs a neutron and forms uranium-239:
The uranium-239 nucleus is unstable and undergoes beta decay to form neptunium-239:
The neptunium-239 nucleus subsequently undergoes another beta decay and forms plutonium-239:
Thus, the overall breeding process can be represented as:
The plutonium-239 produced in this process is a fissile material. It can absorb a neutron and undergo fission, releasing a large amount of energy and additional neutrons:
A breeder reactor therefore performs two important functions: it produces fissile fuel from fertile material and generates nuclear energy. The ratio of the amount of fissile material produced to the amount consumed is called the breeding ratio.
For a breeder reactor, the breeding ratio is greater than unity, meaning that more fissile material is produced than is consumed.
Power Reactors: A power reactor is a nuclear reactor designed primarily to produce useful thermal energy, which is converted into electrical energy. Controlled nuclear fission takes place in the reactor core and releases a large amount of heat.
The heat produced by fission is transferred to a coolant and used to produce steam. The steam drives a turbine, and the turbine rotates an electrical generator.
The power generated by a nuclear reactor depends on the number of nuclear fissions occurring per second and the energy released in each fission. If R is the number of fissions occurring per second and Ef is the energy released per fission, then the thermal power generated is
For a typical fission of uranium-235, the energy released is approximately 200 MeV.
Using the conversion 1 eV = 1.6 × 10−19 J, the energy released per fission is approximately
For example, if a reactor produces 1020 fissions per second, the power generated is
Thus, approximately 3.2 GW of thermal power is generated by the reactor in this example. The electrical power obtained from the plant is lower because only a fraction of the thermal energy can be converted into electrical energy.
Therefore, breeder reactors are mainly designed to produce additional fissile fuel along with energy, whereas power reactors are primarily designed to generate useful energy, especially electrical power.
Uses of Nuclear Reactors
Nuclear reactors have several important applications in power generation, medicine, industry, agriculture, scientific research and other fields. The major uses are:
- Generation of Electrical Power: Nuclear reactors are widely used in nuclear power plants to produce heat through controlled fission and convert it into electrical energy.
- Production of Radioisotopes: Reactors are used to produce useful radioisotopes such as cobalt-60, iodine-131 and other isotopes used in medicine, industry and scientific research.
- Medical Applications: Radioisotopes produced in reactors are used for the diagnosis and treatment of certain diseases, including some forms of cancer.
- Scientific Research: Nuclear reactors provide neutrons and other radiation for studying nuclear reactions, materials, structures and fundamental properties of matter.
- Industrial Applications: Radiation and radioisotopes produced using reactors are used for industrial radiography, thickness measurement, quality control, tracing and detection of defects in materials.
- Agricultural Applications: Radiation and radioisotopes are used in agricultural research, including studies of nutrient absorption, plant growth and the development of improved crop varieties.
- Production of Nuclear Fuel: Breeder reactors can convert fertile materials such as uranium-238 into fissile materials such as plutonium-239, thereby producing additional nuclear fuel.
- Production of Neutrons: Reactors provide intense neutron sources for scientific experiments, neutron activation analysis and other research applications.
- Desalination and Process Heat: The heat produced by nuclear reactors can be used for desalination of seawater and for supplying heat for certain industrial processes.
- Propulsion: Nuclear reactors can be used as energy sources for the propulsion of certain naval vessels, particularly submarines and aircraft carriers.
Thus, nuclear reactors are important not only for generating electricity but also for producing radioisotopes, supporting scientific research, and providing useful applications in medicine, agriculture and industry.
Nuclear Fusion
Nuclear fusion is the process in which two or more light atomic nuclei combine to form a heavier nucleus, accompanied by the release of a very large amount of energy.
In a fusion reaction, two light nuclei come sufficiently close to one another that the strong nuclear force becomes effective and binds them together to form a heavier nucleus. The mass of the products is slightly less than the total mass of the original nuclei. This loss of mass is converted into energy according to Einstein’s mass-energy relation.
The energy released in a nuclear fusion reaction can therefore be calculated from the mass defect:
When the mass defect is expressed in atomic mass units (u), the energy released is given by
Why is very high temperature required? The nuclei taking part in fusion are positively charged and therefore repel each other due to electrostatic or Coulomb force. They must possess sufficiently high kinetic energy to approach one another closely enough for the strong nuclear force to overcome this repulsion.
At extremely high temperatures, matter exists in the form of plasma, a hot ionised state in which atoms are separated into positively charged nuclei and electrons. The high thermal energy of the nuclei increases the probability of successful fusion collisions.
Therefore, a successful fusion reaction requires very high temperature, sufficient particle density and adequate confinement time so that the nuclei have a reasonable probability of undergoing fusion before the plasma loses its energy.
Example of nuclear fusion: One of the most important fusion reactions involves the isotopes deuterium and tritium of hydrogen. They combine to form helium and a neutron:
In this reaction, deuterium has a mass number of 2 and tritium has a mass number of 3. They combine to form helium-4 and a neutron. The total charge and total nucleon number are conserved:
The energy released in the deuterium-tritium reaction is approximately 17.6 MeV, which appears mainly as kinetic energy of the helium nucleus and neutron.
Another example of fusion is the combination of two deuterium nuclei. Several reaction channels are possible. One important reaction is
Fusion reactions are highly exoergic because the products have greater binding energy per nucleon than the original light nuclei. The increase in binding energy is accompanied by a decrease in mass, and the corresponding mass difference appears as released energy.
Fusion in stars: Nuclear fusion is the fundamental source of energy in the Sun and other stars. Under the enormous temperature and pressure existing in stellar interiors, hydrogen nuclei undergo a series of fusion reactions and ultimately form helium, releasing vast amounts of energy.
Controlled nuclear fusion: On Earth, scientists aim to reproduce fusion under controlled conditions so that the released energy can be used as a practical source of power. Since a fusion plasma has extremely high temperature, it cannot be allowed to come into direct contact with ordinary material walls.
Two major approaches to controlled fusion are magnetic confinement and inertial confinement. In magnetic confinement, strong magnetic fields are used to confine the hot plasma. In inertial confinement, very intense energy pulses are used to compress a small fuel pellet to extremely high temperature and density for a short time.
Advantages of nuclear fusion include the enormous energy available from light nuclei, the availability of hydrogen isotopes such as deuterium, and the absence of a sustained chain reaction of the type involved in nuclear fission reactors. However, achieving and maintaining the extreme conditions required for controlled fusion is technically challenging.
Thus, nuclear fusion is the joining of light nuclei to form a heavier nucleus with the release of enormous energy due to the conversion of a small amount of mass into energy.
Energy of the Sun and Stars
The enormous energy radiated by the Sun and other stars is produced mainly by nuclear fusion reactions occurring in their extremely hot and dense interiors.
The central region of a star has an extremely high temperature and enormous pressure. Under these conditions, light nuclei such as hydrogen nuclei possess sufficient kinetic energy to approach one another closely enough for the strong nuclear force to bind them together. Thus, nuclear fusion can take place continuously in the stellar interior.
In the Sun, hydrogen nuclei ultimately combine to form helium. The mass of the helium nucleus formed is slightly less than the total mass of the hydrogen nuclei from which it is formed. This difference in mass is called mass defect and is converted into energy according to Einstein’s mass-energy relation.
The overall fusion process in the Sun can be represented approximately by
The positrons produced in the reactions subsequently annihilate with electrons, producing additional energy in the form of electromagnetic radiation. The neutrinos escape from the Sun and carry away part of the released energy.
The energy produced in the core is transferred outward through the layers of the Sun and is eventually emitted from its surface as electromagnetic radiation, including visible light, infrared radiation and ultraviolet radiation. A small fraction of this energy reaches Earth and provides the energy necessary for almost all life and many natural processes on our planet.
The enormous energy output of the Sun is possible because an extremely large number of fusion reactions occur every second. Although the mass converted into energy in each individual reaction is very small, the total number of reactions is enormous.
The Sun and other stars remain stable for long periods because the inward gravitational force is balanced by the pressure produced by the extremely hot matter and the energy released by nuclear processes in their interiors.
The detailed nuclear processes by which hydrogen is converted into helium in stars occur through different reaction sequences. In the Sun, the proton-proton cycle is the principal energy-producing process, while the carbon-nitrogen cycle is important in hotter and more massive stars.
Thus, the Sun and stars shine because nuclear fusion converts a small amount of nuclear mass into an enormous amount of energy, which ultimately emerges from their surfaces as radiation.
Carbon-Nitrogen Cycle
The Carbon-Nitrogen Cycle, commonly called the CNO cycle, is a series of nuclear fusion reactions in which hydrogen nuclei are converted into helium through a cyclic sequence involving carbon, nitrogen and oxygen nuclei.
The CNO cycle is an important source of energy in the cores of hotter stars. In this process, carbon and nitrogen nuclei participate in the intermediate reactions but are regenerated at the end of the cycle. Therefore, they act as catalysts for the conversion of hydrogen into helium.
The cycle begins with a carbon-12 nucleus absorbing a proton. The six principal nuclear reactions of the CNO-I cycle are:
The carbon-12 nucleus that appears in the last reaction is regenerated and can begin the cycle again. Thus, carbon is not consumed overall. Nitrogen and oxygen nuclei also occur as intermediate products, while the overall transformation is the conversion of hydrogen into helium.
Adding all six reactions and cancelling the intermediate nuclei gives the net reaction:
The two positrons produced in the cycle subsequently annihilate with electrons in the stellar plasma, producing additional electromagnetic radiation. When this annihilation energy is included, the net energy released per complete CNO cycle is approximately 26.7 MeV. 2
In joules, this energy is approximately
The CNO cycle requires extremely high temperatures because the positively charged nuclei must overcome their mutual Coulomb repulsion. It becomes an important hydrogen-burning process at core temperatures of roughly 15–20 million K, and its relative importance increases very rapidly with temperature. The present Sun, with a core temperature of about 15 million K, obtains only a small fraction of its energy from the CNO cycle, whereas the cycle becomes the dominant hydrogen-burning mechanism in sufficiently hotter and more massive main-sequence stars. 3
The CNO cycle is highly temperature sensitive. Therefore, a relatively small increase in the core temperature can produce a much larger increase in the rate of energy generation through the CNO process.
The gamma rays produced in the proton-capture reactions contribute to the energy of the stellar plasma, while the neutrinos produced in the beta-plus decays interact extremely weakly with matter and escape from the star much more readily than ordinary radiation.
Thus, the Carbon-Nitrogen Cycle is a catalytic nuclear-fusion process in which carbon is regenerated at the end of the cycle, four hydrogen nuclei are ultimately converted into one helium nucleus, and approximately 26.7 MeV of energy is released per complete cycle.
Proton-Proton Cycle
The Proton-Proton Cycle, commonly called the pp cycle, is a series of nuclear fusion reactions through which hydrogen nuclei are converted into a helium nucleus with the release of a very large amount of energy.
Stars are formed by the condensation of a large amount of matter under the influence of gravitational attraction. As the matter contracts, its temperature and pressure increase enormously. When the temperature in the stellar interior becomes sufficiently high, the thermal energy of the protons enables nuclear fusion reactions to occur.
The proton-proton cycle is the principal source of energy in the Sun and other stars of similar mass. It is also important in low-mass stars such as red dwarfs. The process ultimately converts four hydrogen nuclei into one helium-4 nucleus.
The first step of the cycle occurs when two protons combine. In this reaction, one proton is converted into a neutron through the weak interaction, producing a deuterium nucleus, a positron and an electron neutrino:
The deuterium nucleus then combines with another proton to form helium-3 and emits a gamma photon:
The above two reactions each occur twice. Thus, two helium-3 nuclei are produced. These two helium-3 nuclei then combine to form a helium-4 nucleus and release two protons:
The two protons released in the last reaction are returned to the stellar plasma and can take part in further proton-proton reactions. Therefore, the process forms a cycle.
Since the first two reactions occur twice, the complete sequence may be represented as:
On adding these reactions and cancelling the intermediate nuclei and the two regenerated protons, the net reaction is
The mass of the helium-4 nucleus formed is slightly less than the total mass of the four hydrogen nuclei taking part in the process. This difference in mass is called mass defect and is converted into energy according to Einstein’s mass-energy relation:
The total energy released in the complete proton-proton cycle is approximately 26.7 MeV.
In joules, this corresponds to approximately
Approximately 0.7% of the total mass of the reacting hydrogen is converted into energy. Although this fraction is small, the enormous number of fusion reactions occurring continuously in the cores of stars produces an immense amount of energy.
Temperature required: The proton-proton cycle occurs in the extremely hot and dense interiors of stars. In the Sun, the temperature at the core is approximately 1.5 × 107 K. Such a high temperature gives the protons very large kinetic energies. However, because protons are positively charged and repel one another, quantum tunnelling is also essential for allowing them to approach sufficiently close for nuclear fusion to occur.
The first reaction of the cycle is comparatively slow because it involves the conversion of a proton into a neutron through the weak interaction. This slow reaction is one of the reasons why hydrogen burning in stars proceeds over extremely long periods.
The energy released by the proton-proton cycle is ultimately transported outward through the layers of the star and is radiated from its surface as electromagnetic radiation. In the case of the Sun, a small fraction of this radiation reaches Earth as sunlight and provides the energy necessary for life and many natural processes.
The proton-proton cycle is the dominant hydrogen-burning process in the Sun and in many relatively low-mass stars. More massive and hotter stars obtain most of their hydrogen-burning energy through the Carbon-Nitrogen-Oxygen (CNO) cycle.
The fusion reactions occurring in stars are responsible for their enormous energy output and radiation. The same basic fusion principle can also occur in an uncontrolled manner under extremely intense conditions. An uncontrolled fusion device is known as a hydrogen bomb.
Thus, the Proton-Proton Cycle is a cyclic sequence of nuclear fusion reactions in which four hydrogen nuclei are ultimately converted into one helium-4 nucleus, releasing approximately 26.7 MeV of energy. This process is the principal source of the Sun’s energy and is one of the fundamental nuclear processes responsible for the light and heat emitted by stars.
Elementary Particles
Elementary particles are the fundamental constituents of matter and the basic particles involved in the interactions of nature. They are not known to be made up of smaller particles.
The discovery of the electron, proton and neutron established that atoms are not indivisible. Further experiments showed that protons and neutrons themselves are composed of more fundamental particles called quarks. Modern particle physics describes elementary particles within the framework of the Standard Model of particle physics.
Elementary particles are broadly classified into fermions and bosons. Fermions constitute matter, whereas bosons are associated mainly with the fundamental interactions.
Fermions have half-integral spin and obey the Pauli exclusion principle. They are divided into quarks and leptons.
Leptons are fundamental particles that do not participate in the strong nuclear interaction. The six leptons are the electron, muon, tau and their corresponding neutrinos:
The electron, muon and tau have electric charge −e, whereas neutrinos have zero electric charge. Neutrinos have extremely small masses and interact very weakly with ordinary matter.
Hadrons are particles that participate in the strong interaction. They are composite particles made of quarks. Hadrons are mainly classified into baryons and mesons.
Baryons are hadrons composed of three quarks. The proton and neutron are the most familiar examples:
Mesons are hadrons composed of one quark and one antiquark. Examples include pions and kaons.
The second major class of elementary particles is bosons. Bosons have integral spin and include particles associated with the fundamental interactions. The photon mediates the electromagnetic interaction, gluons mediate the strong interaction, and the W± and Z0 bosons mediate the weak interaction.
Gluons → Strong interaction
W±, Z0 → Weak interaction
The Higgs boson is associated with the Higgs field, whose interaction with elementary particles contributes to the generation of their masses through the Higgs mechanism.
Particles and their corresponding antiparticles have the same mass but opposite values of electric charge and other relevant additive quantum numbers. For example, the antiparticle of the electron is the positron, represented by e+.
When a particle and its antiparticle meet, they may undergo annihilation, in which their rest mass and kinetic energy are converted into other particles. For example:
Thus, elementary-particle physics deals with the fundamental particles of matter and the particles responsible for their interactions. Quarks and leptons form the basic matter particles, while bosons play important roles in mediating the fundamental interactions.
Quarks
Quarks are elementary particles that are fundamental constituents of hadrons such as protons, neutrons and mesons. They possess fractional electric charges and participate in the strong nuclear interaction.
The quark model was proposed independently by Murray Gell-Mann and George Zweig in 1964 to explain the large number of hadrons discovered experimentally. Quarks have not been observed as isolated particles under ordinary conditions because of a property called quark confinement.
There are six types, or flavours, of quarks: up, down, charm, strange, top and bottom.
| Quark | Symbol | Electric Charge |
|---|---|---|
| Up | u | +2e/3 |
| Down | d | −e/3 |
| Charm | c | +2e/3 |
| Strange | s | −e/3 |
| Top | t | +2e/3 |
| Bottom | b | −e/3 |
Thus, quarks occur in two charge groups. The up-type quarks (u, c and t) have charge +2e/3, while the down-type quarks (d, s and b) have charge −e/3.
Every quark has a corresponding antiquark. Antiquarks have the same mass and spin as their corresponding quarks but opposite electric charge and opposite values of other relevant additive quantum numbers. They are represented by placing a bar over the quark symbol, such as ū, d̄, c̄ and s̄.
Baryons are composite particles made up of three quarks. The proton consists of two up quarks and one down quark:
The total electric charge of the proton is therefore
The neutron consists of one up quark and two down quarks:
Its total electric charge is
Mesons are composite particles consisting of one quark and one antiquark. For example, a positively charged pion has the quark composition:
The quark composition of hadrons explains how particles with different charges and other properties can be formed from a small number of fundamental quark types.
Quark confinement means that quarks are not normally observed as isolated particles. They remain bound inside hadrons by the strong interaction, which is mediated by gluons. Unlike the electromagnetic force, the strong interaction between quarks does not simply decrease to zero as the quarks are separated. As an attempt is made to separate quarks, the energy stored in the strong field increases and can lead to the production of new quark-antiquark pairs rather than an isolated quark.
Quarks also possess a type of strong-interaction charge called colour charge. The three colour labels are conventionally called red, green and blue. These names do not refer to visible colours. Hadrons occur in combinations that are overall colour neutral.
The strong interaction between quarks is described by quantum chromodynamics (QCD). Gluons are the gauge bosons of the strong interaction and are responsible for transmitting the colour force between quarks.
Thus, quarks are fundamental constituents of hadrons. The six quark flavours combine in different ways to form baryons and mesons, while their fractional charges and strong interactions provide the underlying structure of a large number of particles observed in nature.