Nuclear Physics
Nuclear physics is the branch of physics that deals with the atomic nucleus, that is, its composition, its size and mass, the forces that bind its constituents together, and the changes it undergoes through radioactivity, fission and fusion. While atomic physics studies the electrons that surround the nucleus, nuclear physics focuses on the protons and neutrons inside it and on the enormous energy that is released when the nucleus is rearranged. The subject explains how a tiny nucleus can store and liberate millions of times more energy than any chemical reaction. This topic is extremely important for competitive examinations in Assam such as APSC, Assam Police, SSC, and many state and central recruitment tests, because questions on radioactivity, half-life, binding energy, fission, fusion and nuclear reactors appear regularly in general science and physics papers. A clear understanding also links physics with chemistry, medicine, energy production and national security.
Basic Terms
- Nucleus: The small, dense, positively charged central core of an atom that contains protons and neutrons and holds almost the entire mass of the atom.
- Nucleon: A general name for a proton or a neutron, that is, any particle found inside the nucleus.
- Atomic number (Z): The number of protons in the nucleus; it fixes the identity of the element and its position in the periodic table.
- Mass number (A): The total number of protons and neutrons in a nucleus, so that A = Z + N, where N is the number of neutrons.
- Isotopes: Atoms of the same element with the same Z but different numbers of neutrons, and therefore different mass numbers A.
- Isobars: Nuclei that have the same mass number A but different atomic numbers Z.
- Isotones: Nuclei that have the same number of neutrons N but different atomic numbers Z.
- Radioactivity: The spontaneous emission of particles or electromagnetic radiation from an unstable nucleus.
- Half-life (T one-half): The time in which exactly half of the nuclei in a radioactive sample decay.
- Binding energy: The energy required to separate a nucleus completely into its individual protons and neutrons.
- Mass defect: The difference between the sum of the masses of the separate nucleons and the actual measured mass of the nucleus.
Core Concepts and Formulas
- Nuclear radius: R = R zero times A raised to the power one-third, with R zero approximately 1.2 times ten to the power minus fifteen metre. The volume of the nucleus is proportional to A.
- Mass defect: delta m equals the quantity Z times m proton plus (A minus Z) times m neutron, minus the mass of the nucleus.
- Einstein mass-energy relation: E = m c squared.
- Binding energy: BE = delta m c squared; using 1 u = 931.5 MeV per c squared, BE in MeV equals delta m in u multiplied by 931.5.
- Average binding energy per nucleon: BE divided by A; this is largest, about 8.8 MeV, near iron with A approximately 56.
- Radioactive decay law: N = N zero times e to the power minus lambda t, where lambda is the decay constant.
- Half-life relation: T one-half = 0.693 divided by lambda, and N = N zero times one-half raised to n, where n = t divided by T one-half.
- Activity: A = lambda N. The SI unit is the becquerel (Bq); 1 Bq is one decay per second, and 1 curie = 3.7 times ten to the power ten Bq.
- Alpha decay: A decreases by 4 and Z decreases by 2. Beta-minus decay: Z increases by 1. Beta-plus decay: Z decreases by 1. Gamma emission: neither A nor Z changes.
- Unit conversions: 1 atomic mass unit (u) = 1.66 times ten to the power minus twenty-seven kilogram = 931.5 MeV per c squared.
- Fission energy: about 200 MeV is released per fission of uranium-235.
Structure and Size of the Nucleus
Rutherford's gold-foil experiment established that nearly all the mass and all the positive charge of an atom are concentrated in a tiny central nucleus. The nucleus occupies only about ten to the power minus fifteen of the volume of the atom, yet it contains more than 99.9 percent of the atomic mass. The radius of a nucleus is measured in femtometres, where one femtometre equals ten to the power minus fifteen metre. The formula R = R zero times A raised to one-third shows that heavier nuclei are not much larger in radius than lighter ones, because the nuclear volume grows only in proportion to the number of nucleons. This constant density is a remarkable property of nuclear matter. The nucleus is held together by the strong nuclear force, which acts between nucleons at very short range and is much stronger than the electrostatic repulsion between protons.
Nuclear Forces and Stability
The strong nuclear force is attractive, short-ranged, charge-independent and saturating. It binds protons and neutrons regardless of charge, but it operates only over distances of a few femtometres. For light stable nuclei the neutron-to-proton ratio is close to one, while for heavy stable nuclei it rises to about one and a half because extra neutrons are needed to dilute the electrostatic repulsion among many protons. Nuclei that lie outside the band of stability are radioactive. The strong force also explains why the average binding energy per nucleon is roughly constant for most nuclei: each nucleon interacts only with its immediate neighbours.
Radioactivity and Types of Decay
Radioactivity was discovered by Henri Becquerel and studied in detail by Marie and Pierre Curie. An unstable nucleus decays by emitting alpha particles, beta particles or gamma rays. An alpha particle is a helium nucleus containing two protons and two neutrons, so alpha emission reduces A by 4 and Z by 2. A beta-minus particle is an electron emitted when a neutron converts into a proton, so Z increases by 1 while A stays the same. A beta-plus particle is a positron emitted when a proton converts into a neutron, so Z decreases by 1. Gamma rays are high-energy photons emitted when an excited nucleus returns to a lower energy state, and they change neither A nor Z. Alpha decay dominates in very heavy nuclei, beta decay occurs when the neutron-to-proton ratio is unbalanced, and gamma emission usually follows other decays.
Half-life and the Decay Law
Radioactive decay is a random process governed by the law N = N zero times e to the power minus lambda t. The decay constant lambda is the probability of decay per unit time and is independent of temperature, pressure and chemical state. The half-life is the time needed for the number of undecayed nuclei to fall to half its initial value, and it is related to the decay constant by T one-half = 0.693 divided by lambda. After n half-lives, the surviving fraction is one-half raised to n. In problem solving, if the time elapsed is a whole number of half-lives, it is easiest to use fractions such as one-half, one-quarter, one-eighth and so on. The mean life is equal to one divided by lambda, which is about 1.44 times the half-life.
Mass Defect, Binding Energy and Stability
The mass of a stable nucleus is always slightly less than the sum of the masses of its separate protons and neutrons. This missing mass, the mass defect, is converted into binding energy according to E = m c squared. A large binding energy per nucleon means a very stable nucleus. The curve of binding energy per nucleon against mass number rises steeply for light nuclei, reaches a broad maximum of about 8.8 MeV per nucleon around iron-56, and then falls slowly for heavy nuclei. This curve is the key to understanding both fission and fusion: energy is released whenever a reaction moves nuclei towards the maximum of the curve, because the products are more tightly bound than the reactants.
Nuclear Fission
Nuclear fission is the splitting of a heavy nucleus into two lighter nuclei of comparable mass, accompanied by the release of a few neutrons and a large amount of energy. When a slow neutron strikes uranium-235, the nucleus becomes unstable and splits, releasing about 200 MeV of energy per event. Because each fission also releases two or three neutrons, a self-sustaining chain reaction becomes possible if the mass of the material exceeds the critical mass. Fission is the working principle of nuclear power plants and of the first atomic bombs. The energy released is millions of times greater than that released in a chemical reaction of the same mass.
Nuclear Fusion
Nuclear fusion is the joining of two light nuclei to form a heavier nucleus with the release of energy. The most important example is the fusion of hydrogen isotopes to form helium, which powers the Sun and other stars. Fusion requires extremely high temperature and pressure so that the nuclei can overcome their mutual electrostatic repulsion and come close enough for the strong force to act. In stars the proton-proton chain converts hydrogen into helium. On Earth, controlled fusion is being researched because it promises abundant, clean energy, but confining the very hot plasma is a major technological challenge. Hydrogen bombs use uncontrolled fusion triggered by a fission device.
Nuclear Reactors and Their Components
A nuclear reactor controls a fission chain reaction to produce useful energy. Its main components are the fuel, usually enriched uranium; the moderator, such as heavy water or graphite, which slows neutrons to make fission more efficient; the control rods, made of cadmium or boron, which absorb neutrons to regulate the reaction; the coolant, which carries heat to a steam generator; and the shielding, which protects workers from radiation. The reactor is kept critical, meaning each fission produces exactly one further fission on average. Safety systems prevent the chain reaction from running out of control.
Applications and Problem-Solving Approach
Nuclear physics has wide applications: nuclear power generation, medical diagnosis and cancer therapy using radioisotopes, carbon dating of archaeological objects using carbon-14, radiography of welds and castings, and smoke detectors. In exams, numerical problems usually ask for the remaining fraction of a sample after a given time, the number of half-lives elapsed, the mass defect, the binding energy per nucleon, or the Q value of a reaction. A reliable method is to first identify the given quantities and the required quantity, then select the appropriate formula, convert all masses consistently into atomic mass units, and finally check that the units and orders of magnitude are sensible.
Common Mistakes to Avoid
- Confusing atomic number with mass number; remember that Z counts protons while A counts protons plus neutrons.
- Mixing up isotopes, isobars and isotones; learn each definition with an example.
- Forgetting that gamma decay changes neither A nor Z, while alpha and beta decay do change them.
- Using the wrong value of R zero in the nuclear radius formula or forgetting the cube root.
- Making arithmetic errors when converting atomic mass units into energy; 1 u equals 931.5 MeV.
- Assuming that decay rate depends on temperature or chemical bonding; it does not.
- Confusing the half-life with the mean life, which is about 1.44 times larger.
- Ignoring the mass of emitted neutrons or electrons in mass-defect calculations.
How to Prepare This Topic
- Learn the basic definitions first: nucleus, nucleon, atomic number, mass number, isotope, isobar, isotone, radioactivity and half-life.
- Memorise the core formulas and constants, especially R = R zero A to the one-third, T one-half = 0.693 over lambda, and 1 u = 931.5 MeV.
- Practice numerical problems on half-life, activity, mass defect and binding energy until the calculations become quick and accurate.
- Draw and remember the binding-energy-per-nucleon curve and use it to explain why both fission and fusion release energy.
- Revise the working of a nuclear reactor and the applications of radioisotopes, and attempt previous-year questions for Assam examinations.
Frequently Asked Questions
What is the difference between atomic number and mass number?
The atomic number Z is the number of protons in the nucleus and identifies the element, while the mass number A is the total number of protons and neutrons. For example, uranium-235 has mass number 235 and atomic number 92, so it contains 92 protons and 143 neutrons.
Why are isotopes of an element chemically similar but physically different?
Isotopes have the same number of electrons and hence the same chemical behaviour, but they differ in nuclear mass and stability, so their physical properties such as density, radioactive behaviour and nuclear reactions differ.
What is meant by the binding energy of a nucleus?
Binding energy is the energy needed to break a nucleus completely into its separate protons and neutrons. It equals the mass defect multiplied by the square of the speed of light, and a higher binding energy per nucleon indicates greater stability.
Give the relation between half-life and decay constant.
The half-life is inversely proportional to the decay constant and is given by T one-half = 0.693 divided by lambda. A large decay constant means rapid decay and a short half-life.
How much energy is released in the fission of one uranium-235 nucleus?
About 200 MeV of energy is released when one uranium-235 nucleus undergoes fission, which is roughly ten million times more energy than is released by burning one atom of carbon in a chemical reaction.