   # Tc-99 is often used in medicine and has a half- life of about 6 hours. If a patient is given 30.0 micrograms of Tc-99, and assuming that none is lost due to other processes besides radioactive decay, how much Tc-99 is left after 24 hours? ### Chemistry In Focus

7th Edition
Tro + 1 other
Publisher: Cengage Learning,
ISBN: 9781337399692

#### Solutions

Chapter
Section ### Chemistry In Focus

7th Edition
Tro + 1 other
Publisher: Cengage Learning,
ISBN: 9781337399692
Chapter 8, Problem 40E
Textbook Problem
193 views

## Tc-99 is often used in medicine and has a half- life of about 6 hours. If a patient is given 30.0 micrograms of Tc-99, and assuming that none is lost due to other processes besides radioactive decay, how much Tc-99 is left after 24 hours?

Interpretation Introduction

Interpretation:

The amount of Tc-99 left after 24 hours is to be determined.

Concept Introduction:

The time required by a radioactive sample to decompose to half of its mass is called its half-life.

In every half-life, the sample is reduced to half of its mass that was taken initially in the current decay.

### Explanation of Solution

The half-life of Tc-99 is 6 hours. Therefore, the number of half-lives of Tc-99 is calculated as follows:

n=246=4

Since, in every half-life, the sample is reduced to half of its mass that was taken initially in the current decay, the initial mass of Tc-99 is 30 μg.

The mass of Tc-99 left after the first half-life (m1) is calculated as follows:

m1=30 μg2=15 μg.

The mass of Tc-99 left after the second half-life (m2) is calculated as follows:

m2=15 μg2=7

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