   Chapter 31, Problem 57PE

Chapter
Section
Textbook Problem

Data from the appendices and the periodic table may be needed for these problems.Natural uranium is 0.7200% 235U and 99.27% 238U. What were the percentages of 235U and 238U in natural uranium when Earth formed 4.5 × 10 9 years age?

To determine

What were the percentages of U235 and U238 in natural uranium when Earth formed 4.5×109 years ago, natural uranium is 0.7200% U235 and 99.27% U238 ?

Explanation

Given info:

Formula used:

Activity,

R=0.693Nt1/2

The number of nuclei N as a function of time is

N=N0eλt

Calculation:

Consider mass of U238 as 99.27 g and U235 as 0.72 g,

N(U238)=99.27238×6.02×1023=2.51×1023atomsN(U235)=0.72235×6.02×1023=1.84×1021atoms

Half-life of U238=4.468×109y and Half-life of U235=7.04×108y

Substituting,

λ(U238)=0.6934.468× 109=1.55×1010y1λ(U235)=0.6937.04× 108=9.84×1010y1

Finding initial number of atoms,

2.51×1023=N0(U238)e1.55× 10 10×4.5× 109N0(U238)=5

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