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An archaeological sample (remains of an animal) containing 14C isotope of Carbon is found to give 10 beta decays per minute per gram of Carbon. It is known that the natural abundance of 14C in organic matter that is in equilibrium with the atmosphere today will give 15 beta decays per minute per gram of Carbon. The half life of 14C is known to be 5730 years. The estimated age of the sample (in years) is
- a)3010
- b)3350
- c)3500
- d)3800
Correct answer is option 'B'. Can you explain this answer?
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An archaeological sample (remains of an animal) containing 14C isotope...
Given:
- The archaeological sample contains 14C isotope of Carbon.
- The sample gives 10 beta decays per minute per gram of Carbon.
- The natural abundance of 14C in organic matter in equilibrium with the atmosphere today gives 15 beta decays per minute per gram of Carbon.
- The half-life of 14C is 5730 years.
To Find:
The estimated age of the sample (in years).
Solution:
Step 1: Understanding Beta Decay and Half-Life
- Beta decay is a type of radioactive decay where a neutron in the nucleus of an atom is converted into a proton, and a beta particle (an electron or positron) is emitted.
- The rate of beta decay is measured in terms of the number of decays per minute per gram of Carbon.
- The half-life of a radioactive isotope is the time it takes for half of the sample to decay.
Step 2: Comparing Sample Decay Rate with Natural Abundance
- The sample is giving 10 beta decays per minute per gram of Carbon.
- The natural abundance of 14C in organic matter in equilibrium with the atmosphere today gives 15 beta decays per minute per gram of Carbon.
- The sample has a lower decay rate compared to the natural abundance, indicating that it is older than the present-day equilibrium.
Step 3: Determining the Age of the Sample
- The half-life of 14C is 5730 years.
- We can use the formula for radioactive decay to calculate the age of the sample:
Age = (t1/2) * ln(N0/N)
Where:
- t1/2 = half-life of the isotope
- N0 = initial number of radioactive atoms
- N = current number of radioactive atoms
- In this case, we can consider N0 as the natural abundance (15 beta decays) and N as the observed decay rate (10 beta decays).
- Plugging in the values:
Age = (5730 years) * ln(15/10) ≈ 3350 years
Step 4: Final Answer
The estimated age of the sample is approximately 3350 years.
Therefore, the correct answer is option 'B'.
- The archaeological sample contains 14C isotope of Carbon.
- The sample gives 10 beta decays per minute per gram of Carbon.
- The natural abundance of 14C in organic matter in equilibrium with the atmosphere today gives 15 beta decays per minute per gram of Carbon.
- The half-life of 14C is 5730 years.
To Find:
The estimated age of the sample (in years).
Solution:
Step 1: Understanding Beta Decay and Half-Life
- Beta decay is a type of radioactive decay where a neutron in the nucleus of an atom is converted into a proton, and a beta particle (an electron or positron) is emitted.
- The rate of beta decay is measured in terms of the number of decays per minute per gram of Carbon.
- The half-life of a radioactive isotope is the time it takes for half of the sample to decay.
Step 2: Comparing Sample Decay Rate with Natural Abundance
- The sample is giving 10 beta decays per minute per gram of Carbon.
- The natural abundance of 14C in organic matter in equilibrium with the atmosphere today gives 15 beta decays per minute per gram of Carbon.
- The sample has a lower decay rate compared to the natural abundance, indicating that it is older than the present-day equilibrium.
Step 3: Determining the Age of the Sample
- The half-life of 14C is 5730 years.
- We can use the formula for radioactive decay to calculate the age of the sample:
Age = (t1/2) * ln(N0/N)
Where:
- t1/2 = half-life of the isotope
- N0 = initial number of radioactive atoms
- N = current number of radioactive atoms
- In this case, we can consider N0 as the natural abundance (15 beta decays) and N as the observed decay rate (10 beta decays).
- Plugging in the values:
Age = (5730 years) * ln(15/10) ≈ 3350 years
Step 4: Final Answer
The estimated age of the sample is approximately 3350 years.
Therefore, the correct answer is option 'B'.
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An archaeological sample (remains of an animal) containing 14C isotope of Carbon is found to give 10 beta decays per minute per gram of Carbon. It is known that the natural abundance of 14C in organic matter that is in equilibrium with the atmosphere today will give 15 beta decays per minute per gram of Carbon. The half life of 14C is known to be 5730 years. The estimated age of the sample (in years) isa)3010b)3350c)3500d)3800Correct answer is option 'B'. Can you explain this answer?
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An archaeological sample (remains of an animal) containing 14C isotope of Carbon is found to give 10 beta decays per minute per gram of Carbon. It is known that the natural abundance of 14C in organic matter that is in equilibrium with the atmosphere today will give 15 beta decays per minute per gram of Carbon. The half life of 14C is known to be 5730 years. The estimated age of the sample (in years) isa)3010b)3350c)3500d)3800Correct answer is option 'B'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about An archaeological sample (remains of an animal) containing 14C isotope of Carbon is found to give 10 beta decays per minute per gram of Carbon. It is known that the natural abundance of 14C in organic matter that is in equilibrium with the atmosphere today will give 15 beta decays per minute per gram of Carbon. The half life of 14C is known to be 5730 years. The estimated age of the sample (in years) isa)3010b)3350c)3500d)3800Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An archaeological sample (remains of an animal) containing 14C isotope of Carbon is found to give 10 beta decays per minute per gram of Carbon. It is known that the natural abundance of 14C in organic matter that is in equilibrium with the atmosphere today will give 15 beta decays per minute per gram of Carbon. The half life of 14C is known to be 5730 years. The estimated age of the sample (in years) isa)3010b)3350c)3500d)3800Correct answer is option 'B'. Can you explain this answer?.
An archaeological sample (remains of an animal) containing 14C isotope of Carbon is found to give 10 beta decays per minute per gram of Carbon. It is known that the natural abundance of 14C in organic matter that is in equilibrium with the atmosphere today will give 15 beta decays per minute per gram of Carbon. The half life of 14C is known to be 5730 years. The estimated age of the sample (in years) isa)3010b)3350c)3500d)3800Correct answer is option 'B'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about An archaeological sample (remains of an animal) containing 14C isotope of Carbon is found to give 10 beta decays per minute per gram of Carbon. It is known that the natural abundance of 14C in organic matter that is in equilibrium with the atmosphere today will give 15 beta decays per minute per gram of Carbon. The half life of 14C is known to be 5730 years. The estimated age of the sample (in years) isa)3010b)3350c)3500d)3800Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An archaeological sample (remains of an animal) containing 14C isotope of Carbon is found to give 10 beta decays per minute per gram of Carbon. It is known that the natural abundance of 14C in organic matter that is in equilibrium with the atmosphere today will give 15 beta decays per minute per gram of Carbon. The half life of 14C is known to be 5730 years. The estimated age of the sample (in years) isa)3010b)3350c)3500d)3800Correct answer is option 'B'. Can you explain this answer?.
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An archaeological sample (remains of an animal) containing 14C isotope of Carbon is found to give 10 beta decays per minute per gram of Carbon. It is known that the natural abundance of 14C in organic matter that is in equilibrium with the atmosphere today will give 15 beta decays per minute per gram of Carbon. The half life of 14C is known to be 5730 years. The estimated age of the sample (in years) isa)3010b)3350c)3500d)3800Correct answer is option 'B'. Can you explain this answer?, a detailed solution for An archaeological sample (remains of an animal) containing 14C isotope of Carbon is found to give 10 beta decays per minute per gram of Carbon. It is known that the natural abundance of 14C in organic matter that is in equilibrium with the atmosphere today will give 15 beta decays per minute per gram of Carbon. The half life of 14C is known to be 5730 years. The estimated age of the sample (in years) isa)3010b)3350c)3500d)3800Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of An archaeological sample (remains of an animal) containing 14C isotope of Carbon is found to give 10 beta decays per minute per gram of Carbon. It is known that the natural abundance of 14C in organic matter that is in equilibrium with the atmosphere today will give 15 beta decays per minute per gram of Carbon. The half life of 14C is known to be 5730 years. The estimated age of the sample (in years) isa)3010b)3350c)3500d)3800Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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