   Chapter 19, Problem 75CWP

Chapter
Section
Textbook Problem

# Iodine-131 has a half-life of 8.0 days. How many days will it take for 174 g of 131I to decay to 83 g of 131I?

Interpretation Introduction

Interpretation:

Half life of Iodine- 131 is given. Number of days taken by 174g of 131I to decay to 83g of 131I is to be calculated.

Concept introduction:

• In radioactive decay, the decomposition of a parent nuclide takes place and a new daughter nuclide is formed.
• Decay constant is the quantity that expresses the rate of decrease of number of atoms of a radioactive element per second.
• Half life of radioactive sample is defined as the time required for the number of nuclides to reach half of the original value.
Explanation

Given

The value of t1/2 is 8days .

The decay constant is calculated by the formula given below.

k=0.693t1/2

Where,

• t1/2 is the half life of nuclide.
• k is decay constant.

Substitute the value of half life in the above formula.

k=0.6938days-1=0.086625days-1_ .

The decay constant is 0.086625days-1_ .

Given

The value of initial amount is 174g

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