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 calculate the age of the wooden tool and the mummy, you can use the concept of radioactive decay.
1) Age of the Wooden Tool:
The half-life of 14C is approximately 5730 years. The ratio of 14C in the wooden tool compared to fresh wood is 11.9%.
Step 1: Convert 11.9% to a decimal (divide by 100): 11.9% = 0.119
Step 2: Calculate the number of half-lives that have passed using the formula:
Number of Half-lives = ln(0.119) / ln(0.5)
Using the natural logarithm (ln) and dividing by ln(0.5), you should find the number of half-lives that have passed.
Step 3: Calculate the age by multiplying the number of half-lives by the half-life of 14C:
Age = (Number of Half-lives) x (5730 years)
2) Age of the Mummy:
The ratio of 14C/12C for living trees is given as 1.23E-12. The activity of the specimen is provided as 1.34 Bq.
Step 1: Calculate the number of 14C atoms in the specimen using the formula:
Number of 14C atoms = (Activity) / (λ)
Where λ is the decay constant, given by ln(2) / (Half-life).
Step 2: Calculate the number of 12C atoms in the specimen by dividing the number of 14C atoms by the ratio of 14C/12C.
Step 3: Calculate the mass of carbon in the specimen by using the formula:
Mass of carbon = (Number of 12C atoms) x (Mass of 12C)
Step 4: Calculate the age using the formula:
Age = ln(Ratio of 14C/12C in the specimen) / (λ)
Using the natural logarithm (ln), divide by decay constant λ to find the age in years.
Note: The mass of 12C is approximately 12 g/mol.
I hope these step-by-step instructions help you!
To determine the age of the old wooden tool and the mummy, we can use the concept of radioactive decay. Carbon-14 (14C) is a radioactive isotope that decays over time, and by comparing the amount of 14C in a sample to a known reference, we can estimate its age.
1) To calculate the age of the wooden tool:
Given that the wooden tool contains only 11.9% of the 14C that a sample of fresh wood would have, we can assume that the remaining 88.1% has decayed over time.
We can use the formula for exponential decay: N(t) = N(0) * e^(-λt), where N(t) is the remaining amount of 14C at time t, N(0) is the initial amount of 14C, λ is the decay constant, and e is the base of the natural logarithm.
Since we want to find the age, t, we need to rearrange the formula as follows: t = (-1 / λ) * ln(N(t) / N(0)).
The decay constant for carbon-14 is approximately 0.693 / half-life. The half-life of carbon-14 is approximately 5730 years.
Using the given information that the wooden tool contains 11.9% of the 14C, we can substitute N(t) / N(0) = 0.119 into the formula to calculate the age, t.
t = (-1 / (0.693 / 5730)) * ln(0.119) ≈ 3240 years
Therefore, the wooden tool is approximately 3240 years old.
2) To calculate the age of the mummy:
Given the amount of carbon (7.02 g) and its specific activity (1.34 Bq), we first need to calculate the initial amount of 14C using the specific activity formula: A = λN, where A is the specific activity, λ is the decay constant, and N is the number of radioactive atoms.
We can rearrange the formula to find N: N = A / λ.
The specific activity is the number of radioactive decays (Bq) per second, while the initial amount of 14C can be calculated from the given information that the ratio of 14C/12C atoms in living trees is 1.23E-12.
N = (1.34 Bq) / (0.693 / (5730 years)) ≈ 1631.42 radioactive atoms
Now, we can use the same exponential decay formula as in the first question to find the age, t. Rearrange the formula as follows: t = (-1 / λ) * ln(N(t) / N(0)).
We need to substitute the ratio of the current amount of 14C to the initial amount, N(t) / N(0), which can be calculated as follows: N(t) / N(0) = (7.02 g) / (1631.42 radioactive atoms).
t = (-1 / (0.693 / 5730)) * ln((7.02 / 1631.42) / (1.23E-12)) ≈ 7745 years
Therefore, the mummy is approximately 7745 years old.