Themes > Science > Chemistry > Nuclear Chemistry > Nuclear Chemistry Index > Kinetics of radioactive decay The decay of a radioactive material obeys first order kinetics. This means that the following equations all apply to radioactive decay: Rate = k*X ln(X0) - ln(X) =k*t k = 0.693/t1/2 Here, X is the amount of radioactive material, k the 1st order rate constant, and t1/2 the half life for the material. You can also define an activity which is a measure of how many readioactive decays occur each second. Example: 146C is a radioactive isotope of carbon with a half life of 5720 years. If you start with 1.00 mole of carbon-14 and wait 1500 years, how much is left? Solution: This requires the last two equations in the list above. The second will give us the amount at any time, but we need the rate constant which we aren't given. The third equation gives a relationship between half life and k: k = 0.693/t1/2 k = 0.693 / 5720 yr k = 1.21*10-4/ yrNow that we have the rate constant, simply use the second equation: our initial amount X0 is 1 mole, so ln(X0) - ln(X) =k*t ln(1.0) - ln(X) = 1.21*10-4 yr*1500 yr 0 - ln(X) = 0.181 ln(X) = -0.181 X = 0.834 moleAbout a sixth of the carbon has decayed. Information provided by: http://learn.chem.vt.edu