Answer to Question #112604 in Physics for Nya

Question

4. Lead-214 has a half-life of 43.5 seconds. What percent of a sample of this isotope would decay after a time equivalent to 4 half-lives?

Answer 1

The radioactive decay law says

$$N(t)=N_02^{-t/t_{1/2}}$$

Hence, the percent of a sample of the Lead-214 isotope that decay after a time equivalent to 4 half-lives

$$N/N_0=2^{-4}=0.0625=6.25\%$$