The half-life for radioactive decay of 14C is 5730 years (it emits β-particles with energy
of 0.16 MeV). An archaeological sample contained wood that had only 72% of the 14C
found in living trees. What is its age?
k = 0.693/t1/2
Calculate k and substitute into the equation below.
ln(No/N) = kt
I would make up a convenient number for No, say 100, which makes N just 72% of that or 72. Calculate t.
thanks DrBob :)
2716 years
To calculate the age of the archaeological sample, we need to use the concept of half-life and the given information that the wood contains only 72% of the 14C found in living trees.
Here's how you can determine the age of the sample:
1. Determine the number of half-lives the sample has undergone:
The fact that the wood contains only 72% of the 14C in living trees means that it has undergone some decay. The remaining 28% represents the fraction of 14C that remains after a certain number of half-lives. We can determine the number of half-lives using the formula:
remaining fraction = (1/2)^(number of half-lives)
Rearranging the formula to solve for the number of half-lives:
(1/2)^(number of half-lives) = remaining fraction
Taking the logarithm of both sides:
log((1/2)^(number of half-lives)) = log(remaining fraction)
(number of half-lives) * log(1/2) = log(remaining fraction)
Solving for the number of half-lives:
number of half-lives = log(remaining fraction) / log(1/2)
In this case, the remaining fraction is 0.72 (72% expressed as a fraction) and the logarithm of 1/2 is approximately -0.6931.
number of half-lives = log(0.72) / log(1/2)
2. Calculate the age of the sample:
Once we know the number of half-lives, we can calculate the age of the sample by multiplying the half-life by the number of half-lives:
age = half-life * number of half-lives
In this case, the half-life for 14C is given as 5730 years, and the calculated number of half-lives can be substituted:
age = 5730 years * number of half-lives
Substitute the calculated value for the number of half-lives obtained in step 1 into the equation.
By following these steps, you can determine the age of the archaeological sample containing wood that has only 72% of the 14C found in living trees.