radioactive disintegration is 1st order reaction. calculate the age of ancient wood piece if it shows a c14 activity of 20% compared to present day wood. if the half change time for c14 is 5600 years
Calculate k from k = 0.693/t1/2 and substitute into the equation below.
ln(No/N) = kt
No = 100%
N = 20%
k from above.
Solve for t
To calculate the age of an ancient wood piece using C14 dating, we need to apply the principles of radioactive decay.
First, let's understand the concept of a 1st order reaction, which describes the decay of radioactive isotopes. The rate of decay of a radioactive substance is directly proportional to the amount of the substance present. In other words, the rate of decay of C14 follows a 1st order reaction.
The half-life of C14 is given as 5600 years, which means that after 5600 years, half of the original C14 will decay.
Now, let's calculate the age of the ancient wood piece using the given information that its C14 activity is 20% compared to present-day wood.
1. Convert the C14 activity to the fraction of remaining C14:
Present-day C14 activity = 100%
Ancient wood C14 activity = 20%
Fraction of remaining C14 = Ancient wood C14 activity / Present-day C14 activity
= 20% / 100%
= 0.20
2. Calculate the number of half-lives that have elapsed:
The formula to calculate the number of half-lives is:
Number of half-lives = (ln(Fraction of remaining C14)) / (ln(0.5))
Number of half-lives = ln(0.20) / ln(0.5)
≈ 2.3219
3. Calculate the age of the ancient wood piece:
Age = Number of half-lives × Half-life time
Age = 2.3219 × 5600 years
≈ 12998.64 years
So, the calculated age of the ancient wood piece is approximately 12998.64 years.