Different isotopes of a given element will have the same chemistry but behave differently in Radioactive isotopes will decay in a regular exponential way such that one-half of a given amount of parent material will decay to form daughter material in a time period called a half-life. When the material is liquid or gaseous, the parent and daughter isotopes can escape, but when the material solidifies, they cannot so the ratio of parent to daughter isotopes is frozen in.The parent isotope can only decay, increasing the amount of daughter isotopes. The number n is the number of half-lives the sample has been decaying.
Assuming that our atmosphere's composition and the cosmic ray flux has not changed significantly in the last few thousand years, you can find the age of the organic material by comparing its carbon-14/carbon-12 ratios to those of now-living plants.
There are several ways to figure out relative ages, that is, if one thing is older than another.
For example, looking at a series of layers in the side of a cliff, the younger layers will be on top of the older layers.
You then subtract this amount from the total amount of daughter atoms in the rock to get the number of decays that have occurred since the rock solified.
Here are the steps: a result of radioactive decay (call that isotope ``B'' for below).