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Age of fossil will be equal to how many half life which is recovered from a rock sediment contains 100 gm of radioactive carbon C14 and 700 gm of stable isotope N 14 in a sample taken from the same rock?
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Age of fossil will be equal to how many half life which is recovered f...
Overview:
To determine the age of a fossil, we can use the concept of half-life. The half-life is the time it takes for half of the radioactive material to decay. By measuring the ratio of radioactive isotope to stable isotope in a sample, we can calculate the number of half-lives that have passed and hence estimate the age of the fossil.
Given information:
- Rock sediment contains 100 gm of radioactive carbon C14 and 700 gm of stable isotope N14 in a sample from the same rock.
Step 1: Calculate the initial ratio:
The initial ratio of C14 to N14 in the sample can be calculated by dividing the mass of C14 by the mass of N14:
Initial ratio = 100 gm / 700 gm = 1/7
Step 2: Determine the half-life of C14:
The half-life of C14 is known to be approximately 5730 years.
Step 3: Calculate the number of half-lives:
To determine the number of half-lives that have passed, we need to compare the current ratio of C14 to N14 with the initial ratio.
Step 3.1: Calculate the current ratio:
Let's assume the current ratio of C14 to N14 is x. We can set up the following equation based on the decay of C14 over time:
x = (1/2)^n
Where n is the number of half-lives that have passed.
Step 3.2: Solve for n:
We can rewrite the equation as:
log(x) = log((1/2)^n)
log(x) = n * log(1/2)
n = log(x) / log(1/2)
Step 3.3: Calculate x:
To calculate x, we can divide the mass of C14 by the mass of N14 in the current sample:
x = 100 gm / 700 gm = 1/7
Step 3.4: Calculate the number of half-lives:
Substituting the value of x into the equation:
n = log(1/7) / log(1/2)
n ≈ 3.8
Therefore, approximately 3.8 half-lives have passed.
Step 4: Calculate the age of the fossil:
To calculate the age of the fossil, we can multiply the number of half-lives by the half-life of C14:
Age = 3.8 * 5730 years
Age ≈ 21774 years
Conclusion:
The age of the fossil recovered from the rock sediment is estimated to be approximately 21774 years. By using the initial ratio of C14 to N14, the known half-life of C14, and the current ratio of C14 to N14, we were able to calculate the number of half-lives that have passed and hence estimate the age of the fossil.
To determine the age of a fossil, we can use the concept of half-life. The half-life is the time it takes for half of the radioactive material to decay. By measuring the ratio of radioactive isotope to stable isotope in a sample, we can calculate the number of half-lives that have passed and hence estimate the age of the fossil.
Given information:
- Rock sediment contains 100 gm of radioactive carbon C14 and 700 gm of stable isotope N14 in a sample from the same rock.
Step 1: Calculate the initial ratio:
The initial ratio of C14 to N14 in the sample can be calculated by dividing the mass of C14 by the mass of N14:
Initial ratio = 100 gm / 700 gm = 1/7
Step 2: Determine the half-life of C14:
The half-life of C14 is known to be approximately 5730 years.
Step 3: Calculate the number of half-lives:
To determine the number of half-lives that have passed, we need to compare the current ratio of C14 to N14 with the initial ratio.
Step 3.1: Calculate the current ratio:
Let's assume the current ratio of C14 to N14 is x. We can set up the following equation based on the decay of C14 over time:
x = (1/2)^n
Where n is the number of half-lives that have passed.
Step 3.2: Solve for n:
We can rewrite the equation as:
log(x) = log((1/2)^n)
log(x) = n * log(1/2)
n = log(x) / log(1/2)
Step 3.3: Calculate x:
To calculate x, we can divide the mass of C14 by the mass of N14 in the current sample:
x = 100 gm / 700 gm = 1/7
Step 3.4: Calculate the number of half-lives:
Substituting the value of x into the equation:
n = log(1/7) / log(1/2)
n ≈ 3.8
Therefore, approximately 3.8 half-lives have passed.
Step 4: Calculate the age of the fossil:
To calculate the age of the fossil, we can multiply the number of half-lives by the half-life of C14:
Age = 3.8 * 5730 years
Age ≈ 21774 years
Conclusion:
The age of the fossil recovered from the rock sediment is estimated to be approximately 21774 years. By using the initial ratio of C14 to N14, the known half-life of C14, and the current ratio of C14 to N14, we were able to calculate the number of half-lives that have passed and hence estimate the age of the fossil.
Community Answer
Age of fossil will be equal to how many half life which is recovered f...
Options are..... (a) 2 HL(b) 3 HL(c) 5HL (d) 4HL
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Age of fossil will be equal to how many half life which is recovered from a rock sediment contains 100 gm of radioactive carbon C14 and 700 gm of stable isotope N 14 in a sample taken from the same rock?
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Age of fossil will be equal to how many half life which is recovered from a rock sediment contains 100 gm of radioactive carbon C14 and 700 gm of stable isotope N 14 in a sample taken from the same rock? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Age of fossil will be equal to how many half life which is recovered from a rock sediment contains 100 gm of radioactive carbon C14 and 700 gm of stable isotope N 14 in a sample taken from the same rock? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Age of fossil will be equal to how many half life which is recovered from a rock sediment contains 100 gm of radioactive carbon C14 and 700 gm of stable isotope N 14 in a sample taken from the same rock? .
Age of fossil will be equal to how many half life which is recovered from a rock sediment contains 100 gm of radioactive carbon C14 and 700 gm of stable isotope N 14 in a sample taken from the same rock? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Age of fossil will be equal to how many half life which is recovered from a rock sediment contains 100 gm of radioactive carbon C14 and 700 gm of stable isotope N 14 in a sample taken from the same rock? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Age of fossil will be equal to how many half life which is recovered from a rock sediment contains 100 gm of radioactive carbon C14 and 700 gm of stable isotope N 14 in a sample taken from the same rock? .
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