The radioactive element Carbon14 has a halflife of 5730 yr T

The radioactive element Carbon-14 has a half-life of 5,730 yr. The ratio of C-14 present in living organic matter is balanced by photosynthesis. However, this balance is lost once the matter dies. After death, the C-14 begins to decay. The percentage of C-14 present in the remains of organic matter can be used to determine its age. The dead sea scrolls were discovered in 1947. Scientists discovered a linen wrapping for one of the scrolls had lost 22.3% of its C-14 at the time it was found.

a) when will the linen only have 50% of its original C-14 remaining? 25% 10%?

b) What percentage of C-14 would be left in the remains of organic material that is 50,000yr old? 100,000yr? is there a time limit to carbon dating? why?

Solution

decay constant = 0.693/5730 =0.0001209

N = Noe^(-0.0001209t)

a) linen only have 50% of its original :

N = 0.5No

0.5 = e^(-0.0001209t)

take log on both sides:

ln(0.5) = (-0.0001209t)

t = 5733.23 years

25% reamining :

0.25Co = Coe^(-0.0001209t)

take log on both sides:

ln(0.25) =-0.0001209t

t = 1146.45 years

10% remaining:

ln(0.1)/-0.0001209 =t

t= 19045.37 years

b) percentage of C-14 would be left in the remains of organic material that is 50,000yr old

N = Noe^(-0.0001209*50,000)

=No(0.002)

% remaining = 0.2

100,000 year

N = Noe^(--0.0001209*100,000)

=No(0.00000561538)

% remaining = 0.00056138