How does radioactive isotopes decay?

They can decay through one of three ways: 
alpha decay
beta decay and
gamma decay
ALPHA- particle with two neutrons and two protons is ejected from the nucleus of the radioactive atom. this particle released is called an alpha particle. Only occurs with heavy metals.
BETA- pretty much when a proton is transformed into a neutron, or vise versa. in a beta minus decay, the nuetron decays into a proton and in a beta plus decay, a proton decays into a neutron
GAMMA- the nucleus changes from a high energy state to a low energy state by releasing electromagnetic radiation (photons). the number of protons and neutrons stay the same during this reaction therefore the element is still the same.