Question A.10: The half-life of tritium is 12.33 years. (Tritium is the hea...
The half-life of tritium is 12.33 years. (Tritium is the heaviest isotope of hydrogen, with a nucleus consisting of a proton and two neutrons.) If a sample contains 3.0 g of tritium initially, how much remains after 20.0 years?
The equation giving the number of nuclei of a radioactive substance as a function of time is
N=N_{0}\left(\frac{1}{2}\right)^{n}
where N is the number of nuclei remaining, N_{0} is the initial number of nuclei, and n the number of half-lives. Note that this equation is an exponential expression with a base of \frac{1}{2} . The number of half-lives is given by n = t / T_{1 / 2}=20.0 yr / 12.33 yr =1.62 . The fractional amount of tritium that remains after 20.0 yr is therefore
\frac{N}{N_{0}}=\left(\frac{1}{2}\right)^{1.62}=0.325
Hence, of the original 3.00 g of tritium, 0.325 × 3.00 g = 0.975 g remains.