(Based on 7.6.33. from the book) The method of carbon dating makes use of the fact that all living organisms contain two isotopes of carbon, carbon-12, denoted 12C (a stable isotope), and carbon-14, denoted 14C (a radioactive isotope). The ratio of the amount of 14C to the amount of 12C is essentially constant in a living organism (approximately 1 to 1 trillion). When an organism dies, the amount of 12C present remains unchanged, but the 14C decays at a rate proportional to the amount present with a half-life of approximately 5700 years. This change in the amount of 14C relative to the amount of 12C makes it possible to estimate the time at which the organism lived. Let A, be the amount of 14C present in some living organism just (a) before it dies. Write an equation for A(t), the amount of 14C present in a dead organism t years after it dies. (b) Suppose that for some fossil found in an archaeological dig the ratio of the amount of 14C to the amount of 12C of is approximately 1 to 5 trillion. What is the approximate age of the fossil? Let Rx 10-12 be the approximate ratio of the amount of 14C to the amount of 12C measured in some fossil (so R = 0.2 in (b)). Show that amount, A(t), of 14C present in this fossil is A, · R. Hint: explain why (c) Ao original amount of 14C 10-12 A(t) current amount of 14C Rx 10-12* (d) Conclude that the age of this fossil is t = -5700 In(R)/In(2). years.
(Based on 7.6.33. from the book) The method of carbon dating makes use of the fact that all living organisms contain two isotopes of carbon, carbon-12, denoted 12C (a stable isotope), and carbon-14, denoted 14C (a radioactive isotope). The ratio of the amount of 14C to the amount of 12C is essentially constant in a living organism (approximately 1 to 1 trillion). When an organism dies, the amount of 12C present remains unchanged, but the 14C decays at a rate proportional to the amount present with a half-life of approximately 5700 years. This change in the amount of 14C relative to the amount of 12C makes it possible to estimate the time at which the organism lived. Let A, be the amount of 14C present in some living organism just (a) before it dies. Write an equation for A(t), the amount of 14C present in a dead organism t years after it dies. (b) Suppose that for some fossil found in an archaeological dig the ratio of the amount of 14C to the amount of 12C of is approximately 1 to 5 trillion. What is the approximate age of the fossil? Let Rx 10-12 be the approximate ratio of the amount of 14C to the amount of 12C measured in some fossil (so R = 0.2 in (b)). Show that amount, A(t), of 14C present in this fossil is A, · R. Hint: explain why (c) Ao original amount of 14C 10-12 A(t) current amount of 14C Rx 10-12* (d) Conclude that the age of this fossil is t = -5700 In(R)/In(2). years.
Chemistry & Chemical Reactivity
10th Edition
ISBN:9781337399074
Author:John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Publisher:John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Chapter25: Nuclear Chemistry
Section: Chapter Questions
Problem 57GQ
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