Alpha decay.
There are three types of radioactive decay, named by the type of particle they produced. All radioactive decay is the result of an unstable nucleus and release energy. The first is the alpha decay, which emits an alpha particle, a positively charged and heavy particle that does not penetrate too well. It was shown that the alpha particle is actually a Helium nucleus, consisting of two protons and two neutrons. When the unstable nucleus emits the alpha particle, the atomic number of the atom decreases by two and the atomic mass number decreases by four.

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   Beta decay.
The beta particle is an electron. When beta decay occurs, a neutron in the nucleus converts into a proton and an electron. The electron is emitted and takes the released energy with it. When it does not carry enough enery, however, the remaining is carried by a small, massless (or very light) neutral particle called the neutrino. The beta particle is therefore negative and more penetrating than the alpha particle.

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   Gamma decay.
The Gamma radiation is unaffected by magnetic field as it travels; therefore it is electrically neutral. It is actually a type of electromagnetic radiation, and not a particle of significant mass. Gamma rays is one of the most energetic types of electromagnetic radiation, because its wavelength is very short and its frequency very high, on the order of 10^18 Hertz (they are therefore invidible to the eye). Gamma radiation often accompanies alpha decay or beta decay, since the nucleus emitting those particles may still be excited, and the gamma ray is the result of the extra energy. Gamma rays are the most penetrating type of radiation.

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   Natural growth.
Radioactive decay obeys the rules of natural (exponential) growth or decay. That is, the rate of decay is directly proportional to the amount of undecayed substance present. (Chemically, the rate of reaction is directly proportional to the amount of unreacted reactant.) Thus, the first derivative of the substance, say, Uranuim (U) with respect to time is proportional to the amount of undecayed U present.
d[U]/dt = k[U].
Solving this gives d[U]/[U] = kdt, or
ln[U] + C = kt, [U] = a*e^(kt), where a is calculated to be the amounf or Uranium at the start of the decay.
A proporty of the exponential graph is that starting at any arbitrarily chosen time, the time it takes for the amount of undecayed Uranium to decrease by half (or any fraction) is the same. This period of time, the time it take for half the sample to undergo radioactive decay, is called the Half-life of that element. After one half-life, the amount of unreacted sample left is alway one half the amount of unreacted sample before that period of time. Thus, if the half life of a particular sample is 10 years, then after 20 years one-quarter of undecayed sample will be left.

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