plexus0208
Nov5-09, 09:33 PM
1. The problem statement, all variables and given/known data
Background info: The first order rate of nuclear decay of an isotope depends only upon the isotope, not its chemical form or temperature. The half-life for decay of carbon-14 is 5730 years. Assume that the amount of C-14 present in the atmosphere as CO2 and therefore in a living organism has been constant for the last 50,000 years. An ancient sample containing C-14 will show fewer disintegrations of the C-14 that is present than a modern sample because the concentration of C-14 is lower in the ancient sample.
If a 1.00 gram sample of wood found in an archaelogical site in Arizona underwent 7.90x103
disintegrations in a given time period (e.g., 20 h) and a modern sample underwent 1.84x104 disintegrations in the same time period, how old is the ancient sample?
2. Relevant equations
First order:
ln[A]t = -kt + ln[A]o
[A]t = e-kt[A]o
ln(([A]o/2)/[A]o) = -kt1/2 = ln(1/2)
or ln2 = kt1/2 = 0.693
3. The attempt at a solution
kt1/2 = 0.693
k = 0.693/5730 = 1.21x10-4
ln[A]t = -kt + ln[A]o
ln[A]t = ?
ln[A]o = ?
Solve for t?
Is this the right equation to use?
Background info: The first order rate of nuclear decay of an isotope depends only upon the isotope, not its chemical form or temperature. The half-life for decay of carbon-14 is 5730 years. Assume that the amount of C-14 present in the atmosphere as CO2 and therefore in a living organism has been constant for the last 50,000 years. An ancient sample containing C-14 will show fewer disintegrations of the C-14 that is present than a modern sample because the concentration of C-14 is lower in the ancient sample.
If a 1.00 gram sample of wood found in an archaelogical site in Arizona underwent 7.90x103
disintegrations in a given time period (e.g., 20 h) and a modern sample underwent 1.84x104 disintegrations in the same time period, how old is the ancient sample?
2. Relevant equations
First order:
ln[A]t = -kt + ln[A]o
[A]t = e-kt[A]o
ln(([A]o/2)/[A]o) = -kt1/2 = ln(1/2)
or ln2 = kt1/2 = 0.693
3. The attempt at a solution
kt1/2 = 0.693
k = 0.693/5730 = 1.21x10-4
ln[A]t = -kt + ln[A]o
ln[A]t = ?
ln[A]o = ?
Solve for t?
Is this the right equation to use?