I've spent over an hour researching Carbon-14 decay for a Calculus problem, but I have one main problem when solving them: how do you solve for the k
value (decay constant)?
Here is the problem
The method of carbon dating makes use of the fact that all living organisms contain two isotopes of carbon, carbon-12, denoted 12C (a stable isotope), and carbon-14, denoted 14C (a radioactive isotope). The ratio of the amount of 14C to the amount of 12C is essentially constant (approximately 1/10,000). When an organism dies, the amount of 12C present remains unchanged, but the 14C decays at a rate proportional to the amount present with a half-life of approximately 5700 years. This change in the amount of 14C relative to the amount of 12C makes it possible to estimate the time at which the organism lived.
A fossil found in an archaeological dig was found to contain 20% of the original amount of 14C. What is the approximate age of the fossil?
So, I'm not completely lost. I'm aware that the equation I need is:
$\frac{[\ln\frac{N}{No}]}{k} * t_{1/2}$
And I find many websites that insert -.693
for k
when referencing Carbon-14 problems, but I have no idea why they use that value. I assume that the "approximately 1/10,000
" part of the problem is significant, but I don't understand why.
Can someone please help me with understanding how to calculate this k
value that some places have as -.693
and some sites have as .0001...
, both referencing Carbon-14 problems?
Thanks!