Geologists often use carbon dating to find the age of rocks and organisms. Carbon-14 has a half-life of 5730 years, so the amount of Carbon-14 is cut in half after every 5730 years.

Graph showing the radioactive decay of Carbon-14. Substituting those values into the equation gives us the following:įinally, dividing the k and the negative gives us an equation for the half-life of a first-order reaction: Since we are trying to find the half-life of the reactant, we can set t as the half-life and as half of the initial concentration: Here, we can move all the natural logs to the left side of the equation: is the concentration of a reactant at time t, ₀ is the initial concentration of the reactant, and k is the rate constant. We can prove this using the integrated first-order rate law: First-order reactions have constant half-lives. First Order Half-Lifeįirst-order reactions, including radioactive decay, are reactions where the rate of reaction is only dependent on the concentration of one reactant. For example, if the starting concentration of a sample is 1M, then the half-life will be the time it takes for the concentration of the sample to decay to 0.5M. Topics Covered in Other ArticlesĪ half-life (t 1/2) is the time it takes half the concentration of a sample to decay. You will also learn what the half-life formula is and how to use it to find the age of a substance. In this article, you will learn what a half-life is, in 0th.

Half life of carbon 14 formula