Chapter 25, Problem 46PS

### 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

# Strontium-90 is a hazardous radioactive isotope that resulted from atmospheric testing of nuclear weapons. A sample of strontium carbonate containing 90Sr is found to have an activity of 1.0 × 103 dpm. One year later, the activity of this sample is 975 dpm.(a) Calculate the half-life of strontium-90 from this information.(b) How long will it take for the activity of this sample to drop to 1.0% of the initial value?

(a)

Interpretation Introduction

Interpretation:

The half-life of Strontium-90 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

GIVEN INFO: Initial activity of strontium-90(A0) =1.0Ã—103dpm.

Activity of strontium-90(A) = 975dpm.

Time = one year (365days).

CALCULATION:

The decay rate constant is calculated as follows,

ln(A/A0)=âˆ’Îšt

ln[975â€‰dpm1.0Ã—103dpm]=âˆ’k(365â€‰days)ln0.975â€‰=âˆ’k(365â€‰days)âˆ’0.02532â€‰=âˆ’k(365â€‰days)k=âˆ’0.02532âˆ’365â€‰days=6

(b)

Interpretation Introduction

Interpretation:

The time required for the activity of sample to drop to 1% of the initial value 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

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