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A wood specimen containing ^ 14 C taken from an ancient site showed 24 counts in 3 minutes per gram of carbon in a detector. However, a fresh wood showed 52 counts in 2 minutes per gram of carbon. Assuming no background signal in the detector and half-life of ^ 14 C as 5730 years. Calculate the age of wood sample.?
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A wood specimen containing ^ 14 C taken from an ancient site showed 24...
Given information:
- Number of counts in ancient wood specimen = 24 counts in 3 minutes per gram of carbon
- Number of counts in fresh wood specimen = 52 counts in 2 minutes per gram of carbon
- Half-life of 14C = 5730 years
Calculation:
1. Calculate the decay constant (λ) using the half-life formula:
- Half-life (T1/2) = ln(2) / λ
- Rearranging the formula, λ = ln(2) / T1/2
- Substituting the given half-life value, λ = ln(2) / 5730
2. Determine the decay constant for the ancient wood specimen:
- Since the number of counts is directly proportional to the amount of radioactive material, we can compare the two counts to find the ratio of carbon remaining in the ancient wood specimen to the fresh wood specimen.
- Let N1 be the initial amount of carbon in the ancient wood specimen and N2 be the initial amount of carbon in the fresh wood specimen.
- The ratio of counts can be written as:
(N1 / N2) = (C1 / C2) * (e^(-λ1*t1) / e^(-λ2*t2))
Where C1 and C2 are the respective counts, t1 and t2 are the respective time intervals, and λ1 and λ2 are the respective decay constants.
- Substituting the given values, the equation becomes:
(N1 / N2) = (24 / 52) * (e^(-λ1*3) / e^(-λ2*2))
Simplifying further, (N1 / N2) = 0.4615 * (e^(-3λ1) / e^(-2λ2))
3. Substitute the value of λ and solve for (N1 / N2):
- (N1 / N2) = 0.4615 * (e^(-3 * ln(2) / 5730) / e^(-2 * ln(2) / 5730))
- Simplifying further, (N1 / N2) = 0.4615 * (e^(-3ln(2) / 5730) / e^(-2ln(2) / 5730))
- Since e^(-ln(x)) = 1 / x, the equation becomes:
(N1 / N2) = 0.4615 * ((1 / 2^(3/5730)) / (1 / 2^(2/5730)))
(N1 / N2) = 0.4615 * (2^(2/5730) / 2^(3/5730))
(N1 / N2) = 0.4615 * (1 / 2^(1/5730))
(N1 / N2) = 0.4615 * (0.999961)
4. Determine the age of the wood sample:
- Based on the ratio of carbon remaining, we can calculate the age of the ancient wood specimen.
- The age of the wood sample is given by the formula:
Age = - (T1/2 / λ) * ln(N1 /
- Number of counts in ancient wood specimen = 24 counts in 3 minutes per gram of carbon
- Number of counts in fresh wood specimen = 52 counts in 2 minutes per gram of carbon
- Half-life of 14C = 5730 years
Calculation:
1. Calculate the decay constant (λ) using the half-life formula:
- Half-life (T1/2) = ln(2) / λ
- Rearranging the formula, λ = ln(2) / T1/2
- Substituting the given half-life value, λ = ln(2) / 5730
2. Determine the decay constant for the ancient wood specimen:
- Since the number of counts is directly proportional to the amount of radioactive material, we can compare the two counts to find the ratio of carbon remaining in the ancient wood specimen to the fresh wood specimen.
- Let N1 be the initial amount of carbon in the ancient wood specimen and N2 be the initial amount of carbon in the fresh wood specimen.
- The ratio of counts can be written as:
(N1 / N2) = (C1 / C2) * (e^(-λ1*t1) / e^(-λ2*t2))
Where C1 and C2 are the respective counts, t1 and t2 are the respective time intervals, and λ1 and λ2 are the respective decay constants.
- Substituting the given values, the equation becomes:
(N1 / N2) = (24 / 52) * (e^(-λ1*3) / e^(-λ2*2))
Simplifying further, (N1 / N2) = 0.4615 * (e^(-3λ1) / e^(-2λ2))
3. Substitute the value of λ and solve for (N1 / N2):
- (N1 / N2) = 0.4615 * (e^(-3 * ln(2) / 5730) / e^(-2 * ln(2) / 5730))
- Simplifying further, (N1 / N2) = 0.4615 * (e^(-3ln(2) / 5730) / e^(-2ln(2) / 5730))
- Since e^(-ln(x)) = 1 / x, the equation becomes:
(N1 / N2) = 0.4615 * ((1 / 2^(3/5730)) / (1 / 2^(2/5730)))
(N1 / N2) = 0.4615 * (2^(2/5730) / 2^(3/5730))
(N1 / N2) = 0.4615 * (1 / 2^(1/5730))
(N1 / N2) = 0.4615 * (0.999961)
4. Determine the age of the wood sample:
- Based on the ratio of carbon remaining, we can calculate the age of the ancient wood specimen.
- The age of the wood sample is given by the formula:
Age = - (T1/2 / λ) * ln(N1 /
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A wood specimen containing ^ 14 C taken from an ancient site showed 24 counts in 3 minutes per gram of carbon in a detector. However, a fresh wood showed 52 counts in 2 minutes per gram of carbon. Assuming no background signal in the detector and half-life of ^ 14 C as 5730 years. Calculate the age of wood sample.?
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A wood specimen containing ^ 14 C taken from an ancient site showed 24 counts in 3 minutes per gram of carbon in a detector. However, a fresh wood showed 52 counts in 2 minutes per gram of carbon. Assuming no background signal in the detector and half-life of ^ 14 C as 5730 years. Calculate the age of wood sample.? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A wood specimen containing ^ 14 C taken from an ancient site showed 24 counts in 3 minutes per gram of carbon in a detector. However, a fresh wood showed 52 counts in 2 minutes per gram of carbon. Assuming no background signal in the detector and half-life of ^ 14 C as 5730 years. Calculate the age of wood sample.? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wood specimen containing ^ 14 C taken from an ancient site showed 24 counts in 3 minutes per gram of carbon in a detector. However, a fresh wood showed 52 counts in 2 minutes per gram of carbon. Assuming no background signal in the detector and half-life of ^ 14 C as 5730 years. Calculate the age of wood sample.?.
A wood specimen containing ^ 14 C taken from an ancient site showed 24 counts in 3 minutes per gram of carbon in a detector. However, a fresh wood showed 52 counts in 2 minutes per gram of carbon. Assuming no background signal in the detector and half-life of ^ 14 C as 5730 years. Calculate the age of wood sample.? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A wood specimen containing ^ 14 C taken from an ancient site showed 24 counts in 3 minutes per gram of carbon in a detector. However, a fresh wood showed 52 counts in 2 minutes per gram of carbon. Assuming no background signal in the detector and half-life of ^ 14 C as 5730 years. Calculate the age of wood sample.? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wood specimen containing ^ 14 C taken from an ancient site showed 24 counts in 3 minutes per gram of carbon in a detector. However, a fresh wood showed 52 counts in 2 minutes per gram of carbon. Assuming no background signal in the detector and half-life of ^ 14 C as 5730 years. Calculate the age of wood sample.?.
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A wood specimen containing ^ 14 C taken from an ancient site showed 24 counts in 3 minutes per gram of carbon in a detector. However, a fresh wood showed 52 counts in 2 minutes per gram of carbon. Assuming no background signal in the detector and half-life of ^ 14 C as 5730 years. Calculate the age of wood sample.?, a detailed solution for A wood specimen containing ^ 14 C taken from an ancient site showed 24 counts in 3 minutes per gram of carbon in a detector. However, a fresh wood showed 52 counts in 2 minutes per gram of carbon. Assuming no background signal in the detector and half-life of ^ 14 C as 5730 years. Calculate the age of wood sample.? has been provided alongside types of A wood specimen containing ^ 14 C taken from an ancient site showed 24 counts in 3 minutes per gram of carbon in a detector. However, a fresh wood showed 52 counts in 2 minutes per gram of carbon. Assuming no background signal in the detector and half-life of ^ 14 C as 5730 years. Calculate the age of wood sample.? theory, EduRev gives you an
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