Chapter 25.8, Problem 3.4ACP

### 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

# The oldest dated meteorites have ages of about 4.5 billion years. What fraction of the initial 87Rb has decayed?

Interpretation Introduction

Interpretation:

The fraction of the initial Rubidium-87 decayed 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 rate constant:

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

Explanation

The age of Rubidium meteorite is 4.5 billion years and the half-life of Rb-87 is 48.8 billion years.

Calculate the rate constant using the equation mentioned below,

t1/2=â€‰0.693kkâ€‰=â€‰0.6934.88â€‰Ã—1010yâ€‰=â€‰1.42â€‰Ã—10âˆ’11yâˆ’1

Fraction of Activity is calculated as shown below,

ln[N]t[N]0â€‰=Â -Â kâ€‰(t)ln[N]t[N]0â€‰=Â -(1

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