Question

Find the missing value for the radioactive isotope. (round your answer to two decimal places.)

Answer 1

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:

$N(t)=N_0\left( \frac{1}{2} \right)^{\left( \frac{t}{t_{1/2}\right)}$

Thus:

$6=N_0\left( \frac{1}{2} \right)^{\left( \frac{1,000}{5,715}\right)} \\ \\ \Rightarrow6=N_0\left( \frac{1}{2} \right)^{(0.175)} \\ \\ \Rightarrow6=0.8858N_0 \\ \\ \Rightarrow N_0= \frac{6}{0.8858} =\bold{6.77g}$