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Alpha Decay

Alpha decay is the emission of neutrons and protons to bring nucleus to a more stable state. So, it always emits two protons and two electrons.

n + ppElement One (E1)

n + p - 4p-2Element Two (E2)

n + ppE1 = n + p - 4p-2E2 + 42He

Notice that it should be He2+, not just He, and the charge of E2 should be 2-, however an interesting phenomenon occurs. When the new element is created, it automatically releases the two electrons. Likewise, almost instantenously, the Helium ion gains two electrons, stabilizing it.

So, an alpha particle is just a He2+ ion, and alpha decay is the emission of a He2+ ion to form another element.

Beta Decay

Sometimes, stabilizing an atom is done by turning neutrons to protons, or vice versa. 
So, there are two cases: a neutron becomes a proton, and a proton becomes a neutron. 

For the first case, an electron is emitted, so essentially, the number of protons increases by 1, and the number of neutrons decreases by 1. So, the mass number stays the same, but the number of protons increases

n + ppE1 -> n-1 + p+1p + 1E2 + e-

In the second case, the nucleus emits something called a positron. A positron has the same mass as an electron, but it has a position charge. This is called positron emission.

n + ppE1 -> n-1 + p+1p + 1E2 + e+

Gamma Decay

This type of decay doesn't change the number of neutrons or protons, however it reconfigures them, which releases a large amount of energy, in the form of a gamma ray, a very high frequency electromagnetic wave.

David Witten

Photoelectric Effect