Question

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?

Answer 1

Answer:

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-

         $N_{t}=N_{0}(\frac{1}{2})^{(\frac{t}{t_{\frac{1}{2}}})}$

Where, $N_{t}$ is amount of radioactive nuclide after "t" time , N_{0} is initial amount of radioactive nuclide and $t_{\frac{1}{2}}$ is half-life of radioactive nuclide

Here N_{0} = 24 mg, N_{t} = 6.0 mg and $t_{\frac{1}{2}}$ = 30.0 years

So, $6.0mg=24mg\times (\frac{1}{2})^{(\frac{t}{30.0years})}$

or, $t=60.0years$

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