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Q.57

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 1238

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Short Answer

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 excreted 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 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

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