   Chapter 19, Problem 63AE

Chapter
Section
Textbook Problem

# Define “third-life” in a similar way to “half-life,” and determine the “third-life” for a nuclide that has a half-life of 31.4 years.

Interpretation Introduction

Interpretation: Half-life of a nuclide is given. Third life of the nuclide is to be defined and determined.

Concept introduction: A process through which a unstable nuclide looses its energy due to excess of protons or neutrons is known as radioactive decay. The cause of instability of a nuclide is its inefficiency in holding the nucleus together.

Half life of radioactive sample is defined as the time required for the number of nuclides to reach half of the original value.

To determine: The third life of the nuclide.

Explanation

Explanation

Half-life t1/2 is 31.4yrs

The decay constant is calculated by the formula,

λ=0.693t1/2

Where

λ is the decay constant.

t1/2 is the half-life.

Substitute the value of t1/2 in the above equation.

λ=0.69331.4yrs-1=0.0220yrs-1_

The decay constant is 0.0220yrs-1_ .

Explanation

The first order integrated rate law is,

ln(n0n)=λt

Where,

n0 is the initial amount of nuclide

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