Cesium-137 has a half-life of about 30 years. given this half-life, we can represent its decay with the exponential decay function a=a0e(ln(0.5)30)t if we begin with 200 mg of cesium-137, how long will it take for the cesium to decay to the point where there is only 1 milligram remaining? round to the closest year.

229 years

Explanation:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

Half life for first order kinetics is given by:

= half life = 30 years

k = rate constant =?

Integrated rate law for first order kinetics is given as:

k = rate constant of the reaction

= Concentration of reactant initially = 200 mg

= Concentration of reactant at time t = 1 mg

Thus time take for the Cesium to decay to the point where there is only 1 milligram remaining is 229 years.