Given that the half life of carbon-14 is 5,715 and that 6 g of the isotope is remaining after 1,000 years, the initial quantity of the isotope is obtained as follows:
Recall that the amount remaining of a radioactive substance with initial quantity No and half life t(1/2) after t years is given by:
[tex]N(t)=N_0\left( \frac{1}{2} \right)^{\left( \frac{t}{t_{1/2}\right)} [/tex]
Thus:
[tex]6=N_0\left( \frac{1}{2} \right)^{\left( \frac{1,000}{5,715}\right)} \\ \\ \Rightarrow6=N_0\left( \frac{1}{2} \right)^{(0.175)} \\ \\ \Rightarrow6=0.8858N_0 \\ \\ \Rightarrow N_0= \frac{6}{0.8858} =\bold{6.77g}[/tex]
