The carbon-14 decay rate of a sample obtained from a young tree is 0.376 disintegration per second per gram?

Question

Another wood sample prepared from an object recovered at an archaeological excavation gives a decay rate of 0.175 disintegration per second per gram of the sample. What is the age of the object?

Answer 1

0.175 / 0.376 = 0.4654, which is a little less than 1/2 (as in a little less than 1 half-life). But, you just can't take the artithmetic ratio of 0.5 / 0.4654, because the decay is exponential, not linear.

The real ratio would be given by the formula:

disintegration rate of old thing = 0.376 * e^(-time/5730)

5730 years is the half-life of C-14
time is in years
0.376 is the initial rate

So plug in 0.175 and solve for time.

0.175 = 0.376 * e^-(time/5730)
0.465425 = e^-(time/5730)
ln(0.465425) = -time/5730

I think you can get it from there.


note: I read your e-mail. Now it's on to the other problem...

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Answer 2

Carbon 14 decays at a slow but steady rate and reverts to nitrogen 14. ... Modern C14 emits about 15 beta radiations per minute per gram of material, ...

Answer 3

activity is just like mass it halves over time
you just need to work out how many times 0.376 is halved to get 0.175, this is the number of half-lives of carbon-14 that have passed.

0.376 = 0.175 * (1/2)^x
0.376/0.175=(1/2)^x
to solve ill use logs but any method including guessing is usable

ln(0.376/0.175)=x*ln(1/2)
x=[ln(0.376)-ln(0.175)]/ln(1/2)
x=[ln(0.376)-ln(0.175)]/-ln(2)
*im not sure whats going on i keep getting ... in formulas so i used ln instead of log but both work
now all you need is the half-life of carbon14, i recommend wiki