Chapter 25.8, Problem 1.1ACP

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# There are two major isotopes of uranium, 235U (half-life 7.038 × 109 yr, 0.720%) and 238U (half-life 4.468 × 1010 yr, 99.274%). What was the relative abundance of 234U two billion years (2.0 × 109 years) ago?

Interpretation Introduction

Interpretation:

The relative abundance of the uranium-235 two billion years ago has to be calculated.

Concept introduction:

Radiocarbon dating: The dynamic equilibrium exists in all living organism by exhaling or inhaling, maintain the same ratio of 12C and 14C that takes in. when the living organism dies, the intake of 14C stops and it’s the ratio no longer exhibits equilibrium; undergoes radioactive decay.

Half-life period: The time required to reduce to half of its initial value.

Formula used to calculate half-life:

t1/2=0.693kwhere,kis rate constant.(or)ln[N]t- ln[N]0= -kt

Explanation

Calculation:

In a 100g sample today, there are 0.720 g of 235U and 99.274 g of 238U.

For 235U,

kâ€‰=â€‰lnâ€‰(2)7.038Ã—109yâ€‰=â€‰9.8486â€‰Ã—10âˆ’11â€‰yâˆ’1lnâ€‰(0.720)â€‰=â€‰âˆ’(9.8486â€‰Ã—10âˆ’11â€‰yâˆ’1)(2.0â€‰â€‰Ã—109â€‰y)â€‰+â€‰lnâ€‰(x)xâ€‰=â€‰0.877â€‰g.

For 238U,

kâ€‰=â€‰lnâ€‰(2)4

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