How long will it take 200 mg of carbon-14 to decay to the point where only 75 mg remain if the half-life is 5770 years?

2 answers

k = 0.693/t1/2
solve for k

Then
ln(No/N) = kt
No = 200 mg
N = 75 mg
k from above
Solve for t = time in years.
you want t where

200*2^(-t/5770) = 75
2^(-t/5770) = 75/200 = 0.375
-t/5770 = log(.375)/log(2)
t = -5770*log(.375)/log(2)
t = 8164 years

Makes sense since 1/2 > .375 > 1/4
so in half lives, 1 < t < 2