Chemistry
posted by Mima .
A fossil is found to have a C14 level of 86% compared to living organisms. How old is the fossil?, (the half life of C14 is 5730 years).

k = 0.693/t_{1/2}
ln(No/N) = kt
I would use 100 for No
and N = 86
k from above
solve for t in years. 
I thought about that, but didn't know the initial and remaining N. Why initial N is 100?

It's a convenient number to pick. You can start with any number you wish as long as you make N = 0.86*No. So it's easy to pick 100% for No which makes N = 86.

The hint they gave us now is that this is a first intigrated order reaction, I do not get it, what the order of the reaction has to do with nuclear chemistry and decay?

The first is the fact that all nuclear decay reactions are first order. That tells you that you can use the ln(No/N) = kt equation and that k = 0.693/t_{1/2}.
Other orders have different equations for t_{1/2} and for time for x amount to decay. In kinetics it makes little difference if we are talking about decay of a radionuclide or decay of N2 and O2 is a reaction of N2 + O2 ==> 2NO except that radionuclide decay is always first order and other reactions may be second order or third order. 
Thanks, I got it right.