   # A 15.0-mCi (millicurie) radioactive source runs for 2.63 hours. How many atoms have disintegrated? ### Chemistry: Principles and Reactions

8th Edition
William L. Masterton + 1 other
Publisher: Cengage Learning
ISBN: 9781305079373

#### Solutions

Chapter
Section ### Chemistry: Principles and Reactions

8th Edition
William L. Masterton + 1 other
Publisher: Cengage Learning
ISBN: 9781305079373
Chapter 18, Problem 22QAP
Textbook Problem
539 views

## A 15.0-mCi (millicurie) radioactive source runs for 2.63 hours. How many atoms have disintegrated?

Interpretation Introduction

Interpretation:

The number of disintegrated atoms should be determined.

Concept introduction:

Activity is defined as the product of rate constant and number of atoms. It is also defined as the rate of decay or expresses number of atoms decays in unit time.

The mathematical expression is given by:

A = kN

Where, A = activity, k = first order rate constant and N = number of radioactive nuclei.

Activity can be expressed in following units:

1 Bq = 1 atom/s

1 Ci = 3.700 × 1010 atoms/s

### Explanation of Solution

Given information:

Activity = 15.0 mCi

Time = 2.63 hrs

First convert the given value of activity in mCi to Ci.

Since, 1 Ci = 1000 mCi.

Thus, 15.0 mCi = 15.0 mCi×1 Ci1000 mCi=15.0×103 Ci

Now, convert the above value in atoms/s.

Activity = 15.0×103×3.7×1010 atoms/s

= 55.5×107 atoms/s

Convert the given value of time in hrs to second.

Since, 1 hr = 3600 s

Thus, time in second = 2.63×3600 s =9468 s

Now for calculating k:

Since, the unit of k is s-1, the formula is given by:

k=1t

Put the value of time in above expression:

k=19468 s=1

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