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AP Chemistry/Nuclear Chemistry
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Nuclear chemistry is just arithmetic with two variables - charge and mass.
proton + electron = neutron
2 protons + 2 neutrons = alpha particle (Helium-4 Nucleus)
electron = beta particle
energy = gamma ray emission
proton = neutron + positron
Nuclear Stability
Anything with 83 protons (Bismuth) or more is radioactive. Small stable molecules have a neutron:proton ratio of approximately 1:1. More massive ones have a ratio of 1.5:1.
Isotopes can also be radioactive, an example of this is carbon-14 which is used in carbon dating only has 6 protons but is radioactive .
Half Life
The half life of an isotope is time it take for half of a sample to decay. It can vary from very small times(fraction of second) to millions of years. Knowing the half life of a substance allows radioactive dating to be done. The relative abundance of the isotopes in a sample compared to the original abundance can be used to determine the age of the specimen.
ln(percent remaining) = -k(time)
half-life = ln(2/k)