carbon dating - explanation of problem?

Question

Carbon dating can be applied to organic materials up to 5.0 x 104 years old. What percentage of the original is present in a sample after this much time? The half-life of is 5730 yr.



a. 0.24%

b. 8.7%

c. 0.0011%

d. 6%

e. 0.89%


I believe the correct answer is 0.0011% but my method definitely took toolong to be the actual method that should have been used.

the element in question is C-14

Edward, you are partially correct; the correct answer is not d.

the first answer is correct - the correct asnwer is 0.24%

Answer 1

radioactive decay can be modeled as
N(t)=N e^(-L t)
N(t) ni=number of atoms decayed fro time t
N - initial number of atoms
e - base of natural algorithm 2.71...
L -time constant
t -time
Note 5x104=5E+4
***************************
First let's find L
N(t)/N=e^(-Lt) take logs on both sides
ln(N(t)/N)= - Lt
since half life = 5730 than (N(t)/N=1/2)
-L=-ln(2)/t
L=ln(2)/5730=1.21e-4
(Edit – correction)
%=N(t)/N x 100 =e^(-Lt) x100=
%=e^(-1.21e-4 x 5.0E+4) x 100= 0.236%

So the answer is (a)

Answer 2

The correct answer is (a).

[(0.5)^((5 x 10^4)/5730)] x 100%

= 0.24%