Question

The half-life of carbon-14 is 5,730 years. A sample is found to have one-eighth the original amount of carbon-14 in it. How old is the sample?

Answer 1

Note that \[m=m_02^{-\frac{t}{T}}\] Therfore, \[t=Tlog_2(\frac{m_0}{m})\]
which, with given data, yields
\[t=5,470\times3=16,410\text{years}\]

Answer 2

Umm @duy11nv if were talking about half life shouldn't the formula be \[M=Mo(\frac{ 1 }{ 2 })^{\frac{ -t }{ h }} \]

where h is the half-life.

I think you used double time? or am I working please explain to me.

Answer 3

@mebs ,your formula says that the mass of the sample will double after one half life! So,it is obviously wrong.

Since the mass of the sample has become 1/8 the original mass. This means that 3 half lives have passed for the sample. So, t=3*half life.

Or,u may use the formula.

Answer 4

mm alright thanks...

Answer 5

Actually I think it says it will half..so

\[\frac{ \log 0.125 }{ \log.05} = \frac{ -t }{ h }\]
\[t = -3\times 5730 = -17190\]

So the age of the sample is actally 17 190 years old. @Diwakar you used 5470 not 5730 as stated in the question..... Could you check your work and my work.

Answer 6

Thank You all for pulling this one together for me. I believe the correct answer was 17,190 Years old...