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Science Chemistry Chemistry: An Atoms-Focused Approach

The ratio of C 14 in 100 B C E old wooden sample to 700 B C E old wooden sample. Solution: The ratio of C 14 in 100 B C E wooden sample to 700 B C E wooden sample is 1.08 : 1 . Explanation: Concept: From Table 21.2 , the half-life of Carbon-14 is 5730 y r . The ratio of C 14 to C 12 can be found by using the relation N t N 0 = ( 0.5 ) t / t 1 / 2 where N t is the final concentration, N 0 is initial concentration, t 1 / 2 is the half-life, and t is the time interval Formulae: N t N 0 = ( 0.5 ) t / t 1 / 2 Given: Half-life of Carbon-14 = 5730 y r Time interval for 700 BCE t 700 C E = 2003 + 700 = 2703 y r Time interval for 100 B C E t 100 C E = 2003 + 100 = 2103 y r Calculations: The ratio of C 14 to C 12 in the sample of 700 B C E is calculated as follows N t N 0 = ( 0.5 ) t / t 1 / 2 C 14 C 12 = ( 0.5 ) 2703 / 5730 = 0.7211 C 14 = 0.7211 C 12 The ratio of C 14 to C 12 in the 100 B C E sample is C 14 C 12 = ( 0.5 ) 2103 / 5730 = 0.7754 C 14 = 0.7754 C 12 The ratio of the concentration of C 14 in the 100 B C E sample and 700 B C E sample is = 0.7754 C 12 0.7211 C 12 = 1.0753 Therefore, the ratio of C 14 in 100 B C E wooden sample to 700 B C E wooden sample is 1.08 : 1 . Conclusion: Using the formula for the first order decay, the ratio of 14 C to 12 C in the sample is calculated.

The ratio of C 14 in 100 B C E old wooden sample to 700 B C E old wooden sample. Solution: The ratio of C 14 in 100 B C E wooden sample to 700 B C E wooden sample is 1.08 : 1 . Explanation: Concept: From Table 21.2 , the half-life of Carbon-14 is 5730 y r . The ratio of C 14 to C 12 can be found by using the relation N t N 0 = ( 0.5 ) t / t 1 / 2 where N t is the final concentration, N 0 is initial concentration, t 1 / 2 is the half-life, and t is the time interval Formulae: N t N 0 = ( 0.5 ) t / t 1 / 2 Given: Half-life of Carbon-14 = 5730 y r Time interval for 700 BCE t 700 C E = 2003 + 700 = 2703 y r Time interval for 100 B C E t 100 C E = 2003 + 100 = 2103 y r Calculations: The ratio of C 14 to C 12 in the sample of 700 B C E is calculated as follows N t N 0 = ( 0.5 ) t / t 1 / 2 C 14 C 12 = ( 0.5 ) 2703 / 5730 = 0.7211 C 14 = 0.7211 C 12 The ratio of C 14 to C 12 in the 100 B C E sample is C 14 C 12 = ( 0.5 ) 2103 / 5730 = 0.7754 C 14 = 0.7754 C 12 The ratio of the concentration of C 14 in the 100 B C E sample and 700 B C E sample is = 0.7754 C 12 0.7211 C 12 = 1.0753 Therefore, the ratio of C 14 in 100 B C E wooden sample to 700 B C E wooden sample is 1.08 : 1 . Conclusion: Using the formula for the first order decay, the ratio of 14 C to 12 C in the sample is calculated.

Solution Summary: The author explains that the ratio of _14C to

Chemistry: An Atoms-Focused Approach

Chemistry: An Atoms-Focused Approach

14th Edition

ISBN: 9780393912340

Author: Thomas R. Gilbert, Rein V. Kirss, Natalie Foster

Publisher: W. W. Norton & Company

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Chemistry: An Atoms-Focused Approach

Ch. 21 - Prob. 21.1VP Ch. 21 - Prob. 21.2VP Ch. 21 - Prob. 21.4VP Ch. 21 - Prob. 21.5VP Ch. 21 - Prob. 21.6VP Ch. 21 - Prob. 21.7VP Ch. 21 - Prob. 21.8VP Ch. 21 - Prob. 21.9VP Ch. 21 - Prob. 21.10VP Ch. 21 - Prob. 21.11VP

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