Question
half life carbon -14 is 5,730 years. If you start out 50 grams, how long will it take until it reaches 2 grams?
Answers
Damon
x = Xi e^-kt
x/Xi = .5 = e^-5730 k
ln .5 = -5730 k
-.69315 = -5730 k
k = 1.21*10^-4
x = Xi e^-1.21*10^-4 t
2 = 50 e^-1.21*10^-4 t
.04 = e^-1.21*10^-4 t
ln .04 = -1.21*10^-4 t
-3.22 = -1.21*10^-4 t
2.66 * 10^4
= 26,600 years
x/Xi = .5 = e^-5730 k
ln .5 = -5730 k
-.69315 = -5730 k
k = 1.21*10^-4
x = Xi e^-1.21*10^-4 t
2 = 50 e^-1.21*10^-4 t
.04 = e^-1.21*10^-4 t
ln .04 = -1.21*10^-4 t
-3.22 = -1.21*10^-4 t
2.66 * 10^4
= 26,600 years