How do I find the half-life of radioactive isotope?

The half-life of a radioactive isotope is the time taken for half of the atoms in a given sample of the isotope to decay. Radioactivity is random and so, half-life is the average time taken for a large number of atoms. 

There are two ways to find the half-life, both come from the decay equation:   N = N₀e^(-λt)      which is an exponential relationship*. 

Where N is the number of atoms of the isotope left at time t and N₀ is the number of atoms when t =0. λ is known as the decay constant and is the probability that an atom will decay per unit time. If you are given the decay constant you may find the half-life T_1/2 by setting N = N₀/2 and rearranging to find t = T_1/2. Or if you are given N and N₀ you may find λ and follow the previous steps.

*Make sure you familiar with exponentials and logs before attempting this topic