Answer to Question #112603 in Atomic and Nuclear Physics for Nya

Question

3. If the half-life of an isotope is 3 years, what fraction of the isotope remains after 4 years? (put fraction in as decimal

Answer 1

The radioactive decay law says

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

Hence, the fraction of the isotope that remains after 4 years

$$N(4)/N_0=2^{-4/3}=0.40$$