half-life

No one can say for sure when a particular nucleus will decay but one can predict how many in a given sample will decay over time. Radioactive elements have a half-life. The half life of any given element is the time that is required for one half of the sample to decay. So if you have 10 grams of a radioactive element, after one half-life there will be 5 grams of the radioactive element left. After another half-life, there will be 2.5 g of the original element left, after another half-life, 1.25 g will be left. The equation for half-life calculations is as follows:

Half life equation
  • AE is the amount of substance left
  • A0 is the original amount of substance
  • t is the elasped time
  • t1/2 is the half-life of the substance




Other variations on the half-life equation are as follows:

time equation

half life equation

An example problem is if you originally had 157 grams of carbon-14 and the half-life of carbon-14 is 5730 years, how much would there be after 2000 years?

example one
There would be 123 grams left.