   Chapter 25, Problem 44PS

Chapter
Section
Textbook Problem

Iodine-131 (t½ = 8.04 days), a β emitter, is used to treat thyroid cancer.(a) Write an equation for the decomposition of 131I.(b) If you ingest a sample of Nal containing 131I, how much time is required for the activity to decrease to 35.0% of its original value?

(a)

Interpretation Introduction

Interpretation:

An equation for the decomposition of Iodine-131 has to be written.

Concept introduction:

Balancing nuclear reaction equation: The balanced nuclear reaction should conserve both mass number and atomic number.

• The sum of the mass numbers of the reactants should be equal to the sum of mass numbers of the products in the reaction.
• The sum of atomic numbers (or the atomic charge) of the reactants should be equal to the sum of atomic numbers (or the atomic charge) of the products in the reaction.
Explanation

The decomposition of Iodine-131 is transmuted into Xenon with emission of beta-particle. The equation is balanced by equating the mass numbers and the atomic numbers from the right and left-hand sides.

The equation is represented as follows,

I53131

(b)

Interpretation Introduction

Interpretation:

The time required for the activity of Idodine-131 to decrease to 35% of its original 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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