JEE Physics Nuclei Notes Set 07

Atom, Nucleus and Nuclear Notation

An atom has a tiny positively charged nucleus (size about \( 10^{-15} \) to \( 10^{-14} \) m) surrounded by electrons in shells; the atom as a whole is neutral. The nucleus contains protons and neutrons, together called nucleons. Z is the number of protons (atomic number), A is the number of nucleons (mass number) and the number of neutrons is N = A − Z. A nuclide is written \( {}^{A}_{Z}\text{X} \).
The shell with number n holds at most \( 2n^2 \) electrons, so the capacities are 2, 8, 18, 32, and so on.

Isotopes, Isobars and Isotones

Radioactivity

Radioactivity is the spontaneous disintegration of unstable nuclei, with emission of alpha, beta or gamma radiation. It is a nuclear property, not an atomic one, because it is unaffected by changes in the electrons. Almost all nuclides with Z greater than 82 are naturally radioactive (uranium, radium, polonium, thorium).
In a magnetic field the radiation splits into three parts: alpha particles bend one way, beta particles bend the other way and by a larger amount, and gamma rays go straight.

Properties of Alpha, Beta and Gamma Radiation

All three affect a photographic plate and cause fluorescence. Beta particles come from the nucleus (a neutron turns into a proton), unlike cathode rays, which come from orbital electrons. Gamma rays are diffracted by crystals like X-rays.

Changes in the Nucleus During Decay

To count the particles emitted in a series, find the alpha particles from the fall in A (divided by 4) and then the beta particles from the remaining difference in Z.

Mass-Energy Equivalence

In every nuclear change the total mass of the products is slightly less than that of the reactants. The lost mass Δm appears as energy: \( E = \Delta m\,c^2 \). 1 kg corresponds to \( 9\times10^{16} \) J, and 1 atomic mass unit corresponds to about 931 MeV.

Nuclear Fission

Fission is the splitting of a heavy nucleus, after capturing a neutron, into two medium nuclei with the release of neutrons and about 190 MeV of energy per nucleus. A typical reaction is \( {}^{235}_{92}\text{U} + {}^{1}_{0}\text{n} \to {}^{144}_{56}\text{Ba} + {}^{89}_{36}\text{Kr} + 3\,{}^{1}_{0}\text{n} + \text{energy} \); the mass defect here is about 0.20 u, giving roughly 186 to 190 MeV. It was first observed by Hahn and Strassmann in 1938.
The released neutrons can cause further fissions, a chain reaction. If uncontrolled, it is an explosion (nuclear bomb). In a reactor, moderators such as graphite or heavy water slow and absorb neutrons, so the reaction proceeds at a steady rate that is used to generate power.

Nuclear Fusion

Fusion is the joining of two light nuclei into a heavier nucleus with release of energy, because the product has less mass than the reactants. It needs very high temperature (about \( 10^7 \) K) and pressure to overcome the repulsion between the positive nuclei. Example: two deuterons give helium-3 and a neutron (3.3 MeV); helium-3 and a deuteron give helium-4 and a proton (18.3 MeV); overall 21.6 MeV from three deuterons.
Per unit mass, fusion releases more energy than fission. Its products are not harmful radioactive waste, but fusion cannot yet be controlled for power; the hydrogen bomb uses uncontrolled fusion.

Uses and Safety

Uses: cobalt-60 gamma rays treat cancer and sterilise equipment; tracers (radio-iodine, radio-sodium) help diagnosis and study of plant growth; carbon-14 dating estimates the age of fossils; beta rays control the thickness of sheets in factories; alpha particles are used as projectiles in nuclear experiments.
Harmful effects: short-term effects (nausea, hair loss), long-term effects (cancer, leukaemia) and genetic damage. Safety: lead-lined aprons and gloves, long tongs, thick lead containers, shielded and airtight reactors with back-up cooling, and burial of nuclear waste in deep sealed stores far from populated areas.