Unit 19: Nuclear and Particle Physics — Short Questions

Binding energy (B.E.) of a nucleus is the work that must be done on the nucleus to break it completely into its separate, free protons and neutrons. It is calculated from the mass defect Δm = (Zmₚ + Nmₙ) − M_nucleus, the difference between the mass of the separate nucleons and the actual mass of the nucleus. This missing mass is converted into energy using Einstein's relation, B.E. = Δmc².

The statement is incorrect. The "probability of decay per unit time" is the decay constant λ, and half-life is related to it by T½ = 0.693/λ, i.e. T½ is inversely proportional to λ. So if λ is doubled, the half-life is halved, not doubled — a more probable (faster) decay means a shorter, not longer, half-life.

Fraction remaining = (1/2)⁴ = 1/16 = 0.0625, i.e. 6.25% of the original sample remains after four half-lives.

Natural uranium contains only about 0.7% of the fissile isotope U-235; the remaining 99.3% is U-238, which does not readily undergo fission with slow neutrons. Since only this very small fraction can sustain a fission chain reaction, natural uranium cannot efficiently run a reactor and must be enriched (to about 2.4–3.0% U-235) before use — this is why it is called a low grade nuclear fuel in its natural state.

Radioactive iodine-131 is used as a tracer to check whether a person's thyroid gland is working properly, since the thyroid selectively absorbs iodine; a diseased or hyperactive gland absorbs more than twice the normal amount. Iodine-131 is also used therapeutically to treat thyroid cancer.

The half-life of a radioactive material is the time taken for the activity (or the number of undecayed nuclei) of a given sample to decrease to half of its starting value.

In a controlled chain reaction, control rods (cadmium or boron) absorb the extra neutrons so that, on average, only one neutron from each fission event causes another fission; the reaction then proceeds at a steady, regulated rate, releasing energy steadily as used in a nuclear reactor. In an uncontrolled chain reaction, more than one neutron from each fission goes on to cause further fission (mass is above critical mass and neutrons are not absorbed); the number of fissions grows very rapidly, releasing a huge amount of energy almost instantaneously, as in an atomic bomb.

In a thermal (fossil fuel) power station, heat is produced by burning coal or oil in a furnace, whereas in a nuclear power station heat is produced by a controlled fission chain reaction in the reactor core. The nuclear station additionally needs a moderator (to slow neutrons), control rods (to regulate the reaction), and thick concrete/steel shielding for radiation protection — none of which a fossil fuel plant needs. A very small mass of nuclear fuel releases a far greater amount of energy than an equivalent mass of coal or oil. Nuclear plants also produce long-lived radioactive waste requiring special disposal (e.g. deep salt mines), whereas fossil fuel plants produce combustion gases and ash. In both cases, however, the heat generated is ultimately used to raise steam that drives a turbine and generator to produce electricity.

Fusion releases more energy per nucleon (and per unit mass of fuel) than fission. Its fuel — isotopes of hydrogen such as deuterium and tritium — is far more abundant and cheap (available from sea water) compared with uranium. Fusion also does not produce the large quantities of highly radioactive, long-lived fission fragments that a fission reactor does, so a fusion reactor would be cleaner and produce much less hazardous waste.

Radioactive decay is exponential, so the activity decreases by the same fraction (not the same fixed amount) in each equal time interval. After the first year, activity = 90% of the original, A₁ = 0.9A₀. In the second year, the activity again falls by 10% of its value at the start of that year: A₂ = 0.9 × A₁ = 0.9 × 0.9A₀ = 0.81A₀. So after another year the activity is 81% of the original value (i.e. it falls by a further 9% of A₀, not another flat 10% of A₀), because the decay constant λ stays the same and acts on the (now smaller) remaining activity.

Fusing nuclei must be brought extremely close together, but since both nuclei are positively charged, there is a strong electrostatic (Coulomb) force of repulsion between them. Overcoming this repulsion requires giving the nuclei very high kinetic energy, which in practice means raising the fuel to an enormous temperature (of the order of 10 million °C) so the nuclei collide at very high speed. Such temperatures are extremely difficult to produce and sustain, and the hot plasma is hard to confine, which is why controlled fusion for continuous power generation has not yet been achieved.

A nuclear reaction involves changes inside the nucleus itself (rearrangement of protons and neutrons), often transforming one element into a different element or isotope, and releases/absorbs energy of the order of MeV per reaction because of mass-energy conversion (E = Δmc²). A chemical reaction, by contrast, involves only the outer (valence) electrons of atoms rearranging to form new bonds; the nuclei and hence the elements remain unchanged, and the energy involved is of the order of eV — millions of times smaller than in a nuclear reaction.