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kramer
3 years ago
10

Dinosaur fossils are often dated by using an element other than carbon, like potassium-40, that has a longer half life (in this

case, approximately 1.25 billion years). suppose the minimum detectable amount is 0.1% and a dinosaur is dated with 40k to be 67 million years old. what is the maximum age of a fossil that we could date using 40k? (round your answer to one decimal place.)
Mathematics
1 answer:
Firlakuza [10]3 years ago
3 0
The amount of substance left of a radioactive element of half life, t_{\frac{1}{2}} after a time, t, is given by:

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

Given that <span>potassium-40 has a half life of approximately 1.25 billion years.

The number of years it will take for 0.1% of potassium-40 to remain is obtained as follows:

0.1=100\left( \frac{1}{2} \right)^ \frac{t}{1.25}} \\  \\ \Rightarrow\left( \frac{1}{2} \right)^ \frac{t}{1.25}}=0.001 \\  \\ \Rightarrow\frac{t}{1.25}\ln\left( \frac{1}{2} \right)=\ln(0.001) \\  \\ \Rightarrow \frac{t}{1.25}= \frac{\ln(0.001)}{\ln\left( \frac{1}{2} \right)} =9.966 \\  \\ t=9.966(1.25)=12.5

Therefore, </span><span>the maximum age of a fossil that we could date using 40k is 12.5 billion years.</span>
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