Question

if this decay has a half - life of 10.2 years, what mass of 60.8 g carbon - 14 will remain after 20.4 years?
____ g
your answer should include 3 significant digits. do not include units in your answer.
enter the answer

Explanation:

Step1: Calculate the number of half - lives

The formula for the number of half - lives \(n=\frac{t}{t_{1/2}}\), where \(t = 20.4\) years and \(t_{1/2}=10.2\) years.
\(n=\frac{20.4}{10.2}=2\)

Step2: Use the radioactive decay formula

The radioactive decay formula is \(N = N_{0}(\frac{1}{2})^{n}\), where \(N_{0}=60.8\) g and \(n = 2\)
\(N=60.8\times(\frac{1}{2})^{2}\)
\(N = 60.8\times\frac{1}{4}\)
\(N=15.2\)

Answer:

15.2