# After four half-lives have elapsed, the amount of a radioactive sample that has decayed is which of the following? a. 1/4 the original amount b. 3/4 the original amount c. 1/16 the original amount d. no correct response

### General, Organic, and Biological C...

7th Edition
H. Stephen Stoker
Publisher: Cengage Learning
ISBN: 9781285853918

### General, Organic, and Biological C...

7th Edition
H. Stephen Stoker
Publisher: Cengage Learning
ISBN: 9781285853918

#### Solutions

Chapter
Section
Chapter 11.4, Problem 3QQ
Textbook Problem

## After four half-lives have elapsed, the amount of a radioactive sample that has decayed is which of the following?a. 1/4 the original amountb. 3/4 the original amountc. 1/16 the original amountd. no correct response

Expert Solution
Interpretation Introduction

Interpretation:

After four half-lives, the amount of decayed sample of the radioactive sample has to be chosen from the given options.

Concept Introduction:

Radioactive nuclides undergo disintegration by emission of radiation.  All the radioactive nuclide do not undergo the decay at a same rate.  Some decay rapidly and others decay very slowly.  The nuclear stability can be quantitatively expressed by using the half-life.

The time required for half quantity of the radioactive substance to undergo decay is known as half-life.  It is represented as t1/2.

### Explanation of Solution

Reason for correct option:

A radioactive sample will disintegrate into half of its initial amount during its half-life period.  The next half-life period decays half of the amount that is present after the first half-life period.  Therefore, 1/4th of the initial amount will be present after two half-lives.  During the third half-life, another half amount of the radioactive nuclide that is present after two half-lives will be decayed.  Therefore, 1/8th of the initial amount will be present after three half-lives elapsed.  During the fourth half-life, another half amount of the radioactive nuclide that is present after three half-lives will be decayed.  Therefore, 1/16th of the initial amount will be present after four half-lives elapsed.  The sample that has decayed is 15/16.

Hence, option (d) is the correct one.

Reason for incorrect options:

Option (a) tells that 1/4 the original amount of radionuclide will be decayed after four half-lives...

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