1) An old wooden tool is found to contain only 11.9 percent of 14C that a sample of fresh wood would. How many years old is the tool?
2) A specimen taken from the wrappings of a mummy contains 7.02 g of carbon and has an activity of 1.34 Bq. How old is the mummy? Determine its age in years assuming that in living trees the ratio of 14C/12C atoms is 1.23E-12.
Please help
To determine the age of the old wooden tool and the mummy, we can use the concept of carbon dating. Carbon dating relies on the decay of carbon-14 (14C) in organic materials to determine their age.
1) Age of the old wooden tool:
We are given that the wooden tool contains only 11.9 percent of the 14C that a sample of fresh wood would contain. This means that the remaining 88.1 percent has decayed over time.
The concept of carbon dating relies on the fact that the half-life of carbon-14 is approximately 5730 years. Half-life refers to the time it takes for half of the unstable atoms to decay. Using this information, we can set up an equation:
Remaining 14C percentage = initial 14C percentage * (1 / 2)^(number of half-lives)
Substituting the given values:
11.9% = 100% * (1 / 2)^(number of half-lives)
To solve for the number of half-lives, we take the logarithm (base 2) of both sides:
log2(11.9%) = log2(100%) - number of half-lives * log2(1 / 2)
To find the number of half-lives, we rearrange the equation:
number of half-lives = (log2(100%) - log2(11.9%)) / log2(1 / 2)
Using a calculator, compute the result of the above expression to find the number of half-lives. Multiply this value by the half-life of carbon-14 (5730 years) to obtain the age of the old wooden tool in years.
2) Age of the mummy:
We are given the amount of carbon (7.02g) and the activity (1.34 Bq) of the sample taken from the mummy's wrappings. Additionally, we know the ratio of 14C/12C atoms in living trees (1.23E-12).
Carbon dating involves comparing the activity of the sample with that of living trees and calculating the age using the decay equation. The activity is directly proportional to the number of 14C atoms present.
First, calculate the number of 14C atoms in the mummy sample using the given activity:
Number of 14C atoms = activity / (decay constant * 14C/12C ratio)
The decay constant is the rate at which 14C decays, and its value can be obtained from the half-life of carbon-14 (5730 years). Therefore:
Number of 14C atoms = activity / (0.693 / half-life * 14C/12C ratio)
Next, calculate the initial number of 14C atoms in the mummy when it was alive:
Initial number of 14C atoms = Number of 14C atoms / (1 - (1 / 2)^(number of half-lives))
Again, using the half-life and the given 14C/12C ratio.
Finally, use the equation from part 1 to calculate the age of the mummy, substituting the initial number of 14C atoms in the equation to find the number of half-lives. Multiply the number of half-lives by the half-life of carbon-14 (5730 years) to obtain the age of the mummy in years.
Note: These calculations can be complex, so it is advisable to use a scientific calculator or online resources for accurate results.