A
calcareous fossil is found to have ¼ of its original 14c activity(
Half life of 14c is 5730 years), its age is therefore
A)
5730
years
B)
1432.5 years
C)
11460 years
D)
22920 years
Solution:
Given that N = No/4
Half-life ($t_{\frac{1}{2}}$)
= 5730 years
Age
of the fossil (t) =?
Formula
$\frac{N}{No}=
\frac{1}{2}^{\frac{t}{t_{\frac{1}{2}}}}$
Substitute the given values in
the above equation
$\frac{N}{No}=
\frac{1}{2}^{\frac{t}{t_{\frac{1}{2}}}}$
$\frac{No}{4No}=
\frac{1}{2}^{\frac{t}{5730}}$
$\frac{1}{4}
= \frac{1}{2}^{\frac{t}{5730}}$
$\log(\frac{1}{4})
= \log(\frac{1}{2})^{\frac{t}{5730}}$
$\frac{t}{5730}=\frac{\log(\frac{1}{4})}{\log(\frac{1}{2})}$
$\frac{t}{5730}=2$
$t=
5730*2$
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