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Q.57

Expert-verified
Found in: Page 1238

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# The rate at which a radioactive tracer is lost from a patient’s body is the rate at which the isotope decays plus the rate at which the element is excreted from the body. Medical experiments have shown that stable isotopes of a particular element are excreted with a 6.0 day half-life. A radioactive isotope of the same element has a half-life of 9.0 days. What is the effective half-life of the isotope, in days, in a patient’s body?

There fore the effective half life of the isotope is 3.6days

See the step by step solution

## Step 1. Introduction

In radioactive decay the unstable nuclie decay first.. if are the decay constant representing each decay processes, then

The total decay rate is

The solution is,

## Step 2. Explanation

Half lifetime(t1/2) is the time within which the nuclei decay to half or it original amount

That is

## Step 3

Here the half lives of the two process are

The half lives of the process can then be combined in the following fashion to obtain the effective half life

## Step 4

The medical experiments

From the medical experiments it has been revealed that the iscope of certain element

There fore the effective half life of the isotope is 3.6days