Living organisms give a Carbon-14 decay rate of 15.3 counts/min for each gram of carbon in the sample. A sample of bristle cone pine wood has a decay rate of 3.20 counts/min per gram of carbon. Calculate the age of the wood from the radiochemical evidence. Carbon-14 has a half-life of 5770 y.
3.2=15.3(1/2)^-t where t is number of halflifes
3.2/15.3=.5^-t
take ln of each side
-1.56=-t ln(.5)
t=1.56470201859/.693147181=2.235
t= 2.235*5770=
check my work
To calculate the age of the wood using the radiochemical evidence, we can utilize the concept of radioactive decay and the half-life of Carbon-14.
First, we need to determine the ratio of the decay rate of the bristle cone pine wood sample to the decay rate of a living organism. The decay rate of a living organism is given as 15.3 counts/min per gram of carbon, while the decay rate of the bristle cone pine wood sample is given as 3.20 counts/min per gram of carbon.
To find the ratio, we divide the decay rate of the wood sample by the decay rate of a living organism:
Ratio = Decay rate of wood sample / Decay rate of living organism
= 3.20 counts/min per gram / 15.3 counts/min per gram
≈ 0.209
Next, we need to determine the number of half-lives that have passed for the Carbon-14 isotope in the bristle cone pine wood sample. Since Carbon-14 has a half-life of 5770 years, we can calculate the number of half-lives using the following formula:
Number of half-lives = (ln Ratio) / (ln 0.5)
Where ln is the natural logarithm function.
Number of half-lives = (ln 0.209) / (ln 0.5)
≈ -1.557 / -0.6931
≈ 2.25
Now, we can calculate the age of the wood sample by multiplying the number of half-lives by the half-life of Carbon-14:
Age = Number of half-lives * Half-life of Carbon-14
= 2.25 * 5770 years
≈ 12,982.5 years
Therefore, based on the radiochemical evidence, the age of the bristle cone pine wood sample is approximately 12,982.5 years.