If the half life is 5700 years, how do you find the percentage of original carbon-14 that remains in a sample after 2476 years have passed?

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If the half life is 5700 years, how do you find the percentage of original carbon-14 that remains in a sample after 2476 years have passed?

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Answer 1 · 2018-03-15T00:21:49

I get $74.1 %$ $74.1%$ of the original amount remaining.

Explanation:

Well, if the half-life of $14^{C}$ $""14^C$ is $5700$ $5700$ years, then that means after $5700$ $5700$ years have happened, there will be half of the original amount, i.e. $50 %$ $50%$ of the original amount of $14^{C}$ $""14^C$ left.

So, after $2476$ $2476$ years, the sample of $14^{C}$ $""14^C$ has evolved:

$\frac{2476}{5700} \approx 43.4 %$ $2476/5700~~43.4%$ of a half-life

A rule to remember is that if $n$ $n$ is the number of half-lives elapsed, there will be $\frac{100}{2^{n}} %$ $100/(2^n)%$ of the original amount of substance remaining. For the source of this information, click here.

So here, $n = 43.4 % = 0.434$ $n=43.4%=0.434$ . Therefore, there will be

$\frac{100}{2^{0.434}}$ $100/(2^0.434)$

$\approx \frac{100}{1.35}$ $~~100/1.35$

$\approx 74.1 %$ $~~74.1%$ of the original amount remaining.

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If the half life is 5700 years, how do you find the percentage of original carbon-14 that remains in a sample after 2476 years have passed?

1 Answer

Explanation:

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