a 500g sample of potassium-40 is left to decay radioactively. after 3.9x10^9 years, about how many grams of potassium-40 are exp

Question

3 years ago

12

ected to remain?

1 answer:

Lerok [7] · Answer 1 · 2022-03-14T01:06:54+03:00

The mass of radioactive isotope left is 62.5 g.

Explanation:

The half-life of potassium-40 is 1.3 billion years, so

$\tau_{1/2}=1.3\cdot 10^9 y$

The mass of a radioactive sample left after a time t is given by the equation

$m(t) = m_0 (\frac{1}{2})^{-\frac{t}{\tau_{1/2}}$

where in this situation, we have:

$m_0 = 500 g$ is the mass of the initial sample of potassium-40

$\tau_{1/2}=1.3\cdot 10^9 y$ is half-life

By substituting

$t=3.9\cdot 10^9 y$ , we find how much potassium-40 is left at that time:

$m=(500)(\frac{1}{2})^{-\frac{3.9\cdot 10^9}{1.3\cdot 10^9}}=62.5 g$

Learn more about radioactive decay here:

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