Explanation Given i. The isotope 238 U decays to 206 Pb with a half-life of 4.47 x 10 9 years ii. Although this decay occurs in many steps, the first step has the longest half-life. iii. The decay of 238 U is considered as follows 238 U 206 Pb + various decay products iv. A rock is found to contain 4.20 mg of 238 U, and 2.135 mg of 206 Pb v. Assume that the rock contained no Pb during its formation, and all the Pb that it now present arose from the decay of 238 U. vi. 1 u = 1.66 x 10 -24 gm 1) Concept Radio-active dating is a useful way to know how old a certain historic or geological sample is by measuring the radioactivity. Isotopes such as 14 C, 40 K, and others have very long half-lives. By measuring the activity now (λN’), we can calculate what must have been the original N in the sample. And working backwards, and using the half-life calculation, we can estimate the age of the sample. Such measurements act like a clock going backwards! 2) Equations i. N U = N U0 e (-λt) ii. T 1/2 = 0.693/λ 3) Calculations (a) To calculate the number of atoms of 238 U in the rock, let is consider the weight in gm of each 238 U atoms. 1 atom of 238 U weighs = 238u x 1.66 x 10 -24 gm = 3.95 x 10 -22 gm The rock contains 4.20 mg of 238 U, which implies it has 4.20 x 10 - 3 g m 3.95 x 10 - 22 g m = 1.06 x 10 19 atoms of 238 U. Thus the number of atoms of 238 U that the rock contains now = 1.06 x 10 19 atoms (b) Similarly, we can calculate the number of 206 Pb atoms in the rock. 1 atom of 206 Pb weighs = 206u x 1.66 x 10 -24 gm = 3.42 x 10 -22 gm The rock contains 2.135 mg of 206 Pb, which implies it has 2.135 x 10 - 3 g m 3

11th Edition

ISBN: 9781119573968

Author: David Halliday

Publisher: WILEY

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Nuclear interactions

In nature, there are certain rules and standards for an interaction. These interactions are universally accepted. There are four types of interactions:

Question

Chapter 42, Problem 61P

To determine

To calculate:

(a) the number of atoms of ²³⁸U that the rock contains now.

(b) the number of atoms of ²⁰⁶Pb that the rock contains now.

(c) the number of atoms of ²³⁸U that the rock contained during its formation.

(d) the age of the rock.

Expert Solution & Answer

Chapter 42 Solutions

Fundamentals Of Physics

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Ch. 42 - Prob. 11Q Ch. 42 - Prob. 12Q Ch. 42 - a Which of the following nuclides are magic:...Ch. 42 - Prob. 14Q Ch. 42 - Prob. 15Q Ch. 42 - Prob. 1P Ch. 42 - Prob. 2P Ch. 42 - A 10.2 MeV Li nucleus is shot directly at the...Ch. 42 - Prob. 4P Ch. 42 - Prob. 5P Ch. 42 - Prob. 6P Ch. 42 - Prob. 7P Ch. 42 - Prob. 8P Ch. 42 - Prob. 9P Ch. 42 - Prob. 10P Ch. 42 - Prob. 11P Ch. 42 - Prob. 12P Ch. 42 - Prob. 13P Ch. 42 - Prob. 14P Ch. 42 - Prob. 15P Ch. 42 - Prob. 16P Ch. 42 - Prob. 17P Ch. 42 - Prob. 18P Ch. 42 - Prob. 19P Ch. 42 - Prob. 20P Ch. 42 - Prob. 21P Ch. 42 - Prob. 22P Ch. 42 - Prob. 23P Ch. 42 - A penny has a mass of 3.0 g. Calculate the energy...Ch. 42 - Prob. 25P Ch. 42 - Prob. 26P Ch. 42 - Prob. 27P Ch. 42 - Prob. 28P Ch. 42 - Prob. 29P Ch. 42 - The half-life of a particular radioactive isotope...Ch. 42 - Prob. 31P Ch. 42 - Prob. 32P Ch. 42 - Prob. 33P Ch. 42 - Calculate the mass of a sample of initially pure...Ch. 42 - Prob. 35P Ch. 42 - Prob. 36P Ch. 42 - Prob. 37P Ch. 42 - A dose of 8.60 Ci of a radioactive isotope is...Ch. 42 - Prob. 39P Ch. 42 - Prob. 40P Ch. 42 - Prob. 41P Ch. 42 - Prob. 42P Ch. 42 - Prob. 43P Ch. 42 - Prob. 44P Ch. 42 - Prob. 45P Ch. 42 - Prob. 46P Ch. 42 - Prob. 47P Ch. 42 - Prob. 48P Ch. 42 - Prob. 49P Ch. 42 - Prob. 50P Ch. 42 - Prob. 51P Ch. 42 - Prob. 52P Ch. 42 - Prob. 53P Ch. 42 - Prob. 54P Ch. 42 - Prob. 55P Ch. 42 - Prob. 56P Ch. 42 - Prob. 57P Ch. 42 - Prob. 58P Ch. 42 - Prob. 59P Ch. 42 - Prob. 60P Ch. 42 - Prob. 61P Ch. 42 - Prob. 62P Ch. 42 - Prob. 63P Ch. 42 - Prob. 64P Ch. 42 - Prob. 65P Ch. 42 - Prob. 66P Ch. 42 - Prob. 67P Ch. 42 - Prob. 68P Ch. 42 - Prob. 69P Ch. 42 - Prob. 70P Ch. 42 - Prob. 71P Ch. 42 - Prob. 72P Ch. 42 - Prob. 73P Ch. 42 - Prob. 74P Ch. 42 - Prob. 75P Ch. 42 - Prob. 76P Ch. 42 - Prob. 77P Ch. 42 - Prob. 78P Ch. 42 - Prob. 79P Ch. 42 - Prob. 80P Ch. 42 - Prob. 81P Ch. 42 - Prob. 82P Ch. 42 - Prob. 83P Ch. 42 - Prob. 84P Ch. 42 - Prob. 85P Ch. 42 - Prob. 86P Ch. 42 - Prob. 87P Ch. 42 - Characteristic nuclear time is a useful but...Ch. 42 - Prob. 89P Ch. 42 - Using a nuclidic chart, write the symbols for a...Ch. 42 - If the unit for atomic mass were defined so that...Ch. 42 - Prob. 92P Ch. 42 - Prob. 93P Ch. 42 - Prob. 94P Ch. 42 - Prob. 95P Ch. 42 - Prob. 96P Ch. 42 - Prob. 97P

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(a) the number of atoms of 238 U that the rock contains now. (b) the number of atoms of 206 Pb that the rock contains now. (c) the number of atoms of 238 U that the rock contained during its formation. (d) the age of the rock.

Solution Summary: The author calculates the number of atoms of 238 U, 206 Pb, and the age of the rock by measuring the radioactivity.

Concept explainers

To calculate:

(a) the number of atoms of ²³⁸U that the rock contains now.

(b) the number of atoms of ²⁰⁶Pb that the rock contains now.

(c) the number of atoms of ²³⁸U that the rock contained during its formation.

(d) the age of the rock.

Chapter 42 Solutions

(a) the number of atoms of 238 U that the rock contains now. (b) the number of atoms of 206 Pb that the rock contains now. (c) the number of atoms of 238 U that the rock contained during its formation. (d) the age of the rock.

Solution Summary: The author calculates the number of atoms of 238 U, 206 Pb, and the age of the rock by measuring the radioactivity.

Concept explainers

To calculate: (a) the number of atoms of 238U that the rock contains now. (b) the number of atoms of 206Pb that the rock contains now. (c) the number of atoms of 238U that the rock contained during its formation. (d) the age of the rock.

Chapter 42 Solutions

To calculate:

(a) the number of atoms of ²³⁸U that the rock contains now.

(b) the number of atoms of ²⁰⁶Pb that the rock contains now.

(c) the number of atoms of ²³⁸U that the rock contained during its formation.

(d) the age of the rock.