The decay of U-238 to Pb-206 can be used to estimate the age of inorganic matter. The half-life of U-238 is 4.5 X 100 years. In a particular rock sample, the ratio of the numbers of Pb-206 to U-238 atoms is 0.66. Assume all of the Pb-206 present is due to the decay of U-238. What is the age of the rock? C=Coe -kt -693 Ty2693 K= = 1.541 X10 -9
The decay of U-238 to Pb-206 can be used to estimate the age of inorganic matter. The half-life of U-238 is 4.5 X 100 years. In a particular rock sample, the ratio of the numbers of Pb-206 to U-238 atoms is 0.66. Assume all of the Pb-206 present is due to the decay of U-238. What is the age of the rock? C=Coe -kt -693 Ty2693 K= = 1.541 X10 -9
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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Transcribed Image Text:The decay of U-238 to Pb-206 can be used to estimate the age of inorganic matter. The half-life
of U-238 is 4.5 X 10⁹ years. In a particular rock sample, the ratio of the numbers of Pb-206 to
U-238 atoms is 0.66. Assume all of the Pb-206 present is due to the decay of U-238. What is
the age of the rock?
-kt
C=Coe
.693
.693
-10
K=
= 1.54 X10
K
4.5 410
Ty2:
:
Expert Solution
Step 1: Assuming some variables
To calculate the age of the rock using the decay of U-238 to Pb-206, you can use the concept of radioactive decay and the half-life of U-238.
The half-life of U-238 is given as 4.5 x 10^9 years, which means that half of the U-238 atoms will decay to Pb-206 in that time period.
First, let's define some variables:
- N0 :The initial number of U-238 atoms in the rock.
- N: The current number of U-238 atoms in the rock.
- t: The age of the rock in years.
- λ: The decay constant (λ = ln( 2) / half-life), which is the rate at which U-238 decays.
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