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Carbon is one of the fundamental elements in everything that's alive on Earth. The three naturally occuring isotopes of carbon are 12C (mass fraction = 0.99), 1BC (mass fraction = 0.01) and radioactive 14C. The relative abundance or mass fraction of 14C is about 10-12 (or 1 in 1012 atoms). This radiocarbon originates from cosmic rays interacting with nitrogen atoms in the atmosphere and has a half-life time of 5730 years. Since it's half-life time is a lot higher than the time the atoms need to go through the carbon cycle, all living biomass at the Earth's surface has the same abundance of 14C as in the atmosphere. After a plant or animal has deceased the amount of 14C atoms will decay exponentially according to the following formula: m(t) · 2-t/t1/2 = mo with mo as the mass fraction at t = 0 and t1/2 as the half-life time. Since we know the abundance of 14C in the atmosphere, we can use this equation to estimate the time of death of an organism. This method is known as carbon dating. Question: It is known that the general limit for carbon dating is about 50.000 years. Calculate the experimental detection limit, mlimit , the lowest detectable fraction of 14C atoms. Round off your answer to two significant figures. Note: do not express this as a percentage! Solution: mįlimit

Carbon is one of the fundamental elements in everything that's alive on Earth. The three naturally occuring isotopes of carbon are 12C (mass fraction = 0.99), 1BC (mass fraction = 0.01) and radioactive 14C. The relative abundance or mass fraction of 14C is about 10-12 (or 1 in 1012 atoms). This radiocarbon originates from cosmic rays interacting with nitrogen atoms in the atmosphere and has a half-life time of 5730 years. Since it's half-life time is a lot higher than the time the atoms need to go through the carbon cycle, all living biomass at the Earth's surface has the same abundance of 14C as in the atmosphere. After a plant or animal has deceased the amount of 14C atoms will decay exponentially according to the following formula: m(t) · 2-t/t1/2 = mo with mo as the mass fraction at t = 0 and t1/2 as the half-life time. Since we know the abundance of 14C in the atmosphere, we can use this equation to estimate the time of death of an organism. This method is known as carbon dating. Question: It is known that the general limit for carbon dating is about 50.000 years. Calculate the experimental detection limit, mlimit , the lowest detectable fraction of 14C atoms. Round off your answer to two significant figures. Note: do not express this as a percentage! Solution: mįlimit

Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter30: Nuclear Physics
Section: Chapter Questions
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Carbon is one of the fundamental elements in everything that's alive on Earth. The three naturally occuring isotopes of carbon are 12C (mass fraction = 0.99), 1³C (mass fraction = 0.01) and radioactive 14C. The relative abundance or mass fraction of 14C is about 10-12 (or 1 in 1012 atoms). This radiocarbon originates from cosmic rays interacting with nitrogen atoms in the atmosphere and has a half-life time of 5730 years. Since it's half-life time is a lot higher than the time the atoms need to go through the carbon cycle, all living biomass at the Earth's surface has the same abundance of 14C as in the atmosphere. After a plant or animal has deceased the amount of 14C atoms will decay exponentially according to the following formula: = mo · 2-t/tı/2 with mo as the mass fraction at t = 0 and t1/2 as the half-life time. Since we know the abundance of 14C in the atmosphere, we can use this equation to estimate the time of death of an organism. This method is known as carbon dating. Question: It is known that the general limit for carbon dating is about 50.000 years. Calculate the experimental detection limit, mlimit, the lowest detectable fraction of 14C atoms. Round off your answer to two significant figures. Note: do not express this as a percentage! Solution: mlimit
Transcribed Image Text:Carbon is one of the fundamental elements in everything that's alive on Earth. The three naturally occuring isotopes of carbon are 12C (mass fraction = 0.99), 1³C (mass fraction = 0.01) and radioactive 14C. The relative abundance or mass fraction of 14C is about 10-12 (or 1 in 1012 atoms). This radiocarbon originates from cosmic rays interacting with nitrogen atoms in the atmosphere and has a half-life time of 5730 years. Since it's half-life time is a lot higher than the time the atoms need to go through the carbon cycle, all living biomass at the Earth's surface has the same abundance of 14C as in the atmosphere. After a plant or animal has deceased the amount of 14C atoms will decay exponentially according to the following formula: = mo · 2-t/tı/2 with mo as the mass fraction at t = 0 and t1/2 as the half-life time. Since we know the abundance of 14C in the atmosphere, we can use this equation to estimate the time of death of an organism. This method is known as carbon dating. Question: It is known that the general limit for carbon dating is about 50.000 years. Calculate the experimental detection limit, mlimit, the lowest detectable fraction of 14C atoms. Round off your answer to two significant figures. Note: do not express this as a percentage! Solution: mlimit
Question: The 14C content of a bone fragment is analysed and it is found that its relative abundance is 10-14. Estimate the age of the bone. Round off your answer to two significant figures. Solution: Age years %3D
Transcribed Image Text:Question: The 14C content of a bone fragment is analysed and it is found that its relative abundance is 10-14. Estimate the age of the bone. Round off your answer to two significant figures. Solution: Age years %3D
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