The mass of radioactive isotope left is 62.5 g.
Explanation:
The half-life of potassium-40 is 1.3 billion years, so
[tex]\tau_{1/2}=1.3\cdot 10^9 y[/tex]
The mass of a radioactive sample left after a time t is given by the equation
[tex]m(t) = m_0 (\frac{1}{2})^{-\frac{t}{\tau_{1/2}}[/tex]
where in this situation, we have:
[tex]m_0 = 500 g[/tex] is the mass of the initial sample of potassium-40
[tex]\tau_{1/2}=1.3\cdot 10^9 y[/tex] is half-life
By substituting
[tex]t=3.9\cdot 10^9 y[/tex], we find how much potassium-40 is left at that time:
[tex]m=(500)(\frac{1}{2})^{-\frac{3.9\cdot 10^9}{1.3\cdot 10^9}}=62.5 g[/tex]
Learn more about radioactive decay here:
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