Quick questions on Nuclear physics and radioactivity: VCE Physics Unit 1 Year 11

Same $Z$ (same element) but different $N$ (and so different $A$). Examples: $^{12}_6$C, $^{13}_6$C, $^{14}_6$C are all carbon, but with different neutron counts.

Emission of a helium nucleus ($^4_2$He). Mass number decreases by 4; atomic number by 2.

A neutron converts to a proton plus electron plus antineutrino. Atomic number increases by 1; mass number unchanged.

A proton converts to a neutron plus positron plus neutrino. (Less common; not always required in Unit 1.)

The nucleus, in an excited state after another decay, emits a high-energy photon. Mass number and atomic number unchanged.

The released neutrons can induce further fissions. If on average more than one neutron per fission triggers a new fission, the chain reaction is supercritical (explosive). Controlled chain reactions (one neutron per fission triggers one new fission) power nuclear reactors.

Fission reactors generate about 10 percent of world electricity. Concerns: waste storage, weapons proliferation, accident risk (Three Mile Island 1979, Chernobyl 1986, Fukushima 2011).

Diagnostic imaging (technetium-99m, fluorine-18 in PET scans). Cancer therapy (cobalt-60, iodine-131, linear accelerators).

Thickness measurement, smoke detectors (americium-241), industrial radiography.

Carbon-14 is produced in the upper atmosphere and incorporated into living things. After death, $^{14}$C content decays with half-life 5,730 years. Used to date objects up to about 50,000 years old.

Mass numbers must balance; charges must balance.

Alpha is heavy and slow; beta is fast and light; gamma is electromagnetic.

$N = N_0 (1/2)^{t/T_{1/2}}$. If $t$ is exactly $n$ half-lives, $N = N_0/2^n$.

Individual decay is random; half-life is statistical.

Common fissile materials are $^{235}$U and $^{239}$Pu, not all uranium isotopes.