Question
A $500 \mathrm{mg}$ sample of rock was found to have $2.45 \times 10^{-6}$ mol of potassium- $40\left(t_{1 / 2}=1.3 \times 10^{9} \mathrm{yr}\right)$ and $2.45 \times$ $10^{-6}$ mol of argon- 40 . How old was the rock?
Step 1
The half-life of potassium-40 is given as $1.3 \times 10^{9}$ years. The equation for the decay constant is: \[k = \frac{\ln(2)}{t_{1/2}}\] Show more…
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A $500 \mathrm{mg}$ sample of rock was found to have $2.45 \times 10^{-6}$ mol of potassium- $40\left(t_{1 / 2}=1.3 \times 10^{9} \mathrm{yr}\right)$ and $2.45 \times$ $10^{-6}$ mol of argon- 40 . How old was the rock? (Hint: What assumption is made about the origin of the argon-40?)
A $0.500 \mathrm{~g}$ sample of rock was found to have $2.45 \times 10^{-6}$ mol of potassium-40 $\left(t_{1 / 2}=1.3 \times 10^{9} \mathrm{yr}\right)$ and $1.22 \times$ $10^{-6} \mathrm{~mol}$ of argon- $40 .$ How old was the rock? (What assumption is made about the origin of the argon-40?)
If a rock sample was found to contain $1.16 \times 10^{-7} \mathrm{~mol}$ of argon-40, how much potassium- $40\left(t_{1 / 2}=1.3 \times 10^{9} \mathrm{yr}\right)$ would also have to be present for the rock to be $1.3 \times 10^{9}$ years old? See assumption in Problem 13.91 .
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