The beta decay of cesium-137 has a half-life of 30.0 years. how many years must pass to reduce a 24 mg sample of cesium 137 to 6.0 mg?

60.0 years must pass to reduce a 24 mg of cesium 237 to 6.0 mg

Explanation:

For radioactive decay of a radioactive nuclide-

Where, is amount of radioactive nuclide after "t" time , N_{0} is initial amount of radioactive nuclide and is half-life of radioactive nuclide

Here N_{0} = 24 mg, N_{t} = 6.0 mg and = 30.0 years

So,

or,

So 60.0 years must pass to reduce a 24 mg of cesium 237 to 6.0 mg