   Chapter 25, Problem 43PS

Chapter
Section
Textbook Problem

Gallium-67 (t½ = 78.25 hours) is used in the medical diagnosis of certain kinds of tumors. If you ingest a compound containing 0.015 mg of this isotope, what mass (in milligrams) remains in your body after 13 days? (Assume none is excreted.)

Interpretation Introduction

Interpretation:

After 13 days, mass of Gallium-67 remains in milligrams has to be calculated.

Concept Introduction:

Radiocarbon dating: The dynamic equilibrium exists in all living organism by exhaling or inhaling, maintain the same ratio of 12C and 14C that takes in. when the living organism dies, the intake of 14C stops and it’s the ratio no longer exhibits equilibrium; undergoes radioactive decay.

Half-life period: The time required to reduce to half of its initial value.

Formula used to calculate half-life:

t1/2=0.693kwhere,kis rate constant.(or)ln[N]t- ln[N]0= -kt

Explanation

Given info:

Half-life of gallium-67(t1/2)=78.25hours

The amount of gallium-67=0.015mg

Time t=13days

Calculation:

The decay rate constant (k) is calculated as follows,

k=0.693t1/2=8.856×103h1(t1/2=78.25hours)

The initial amount (Ao) of Gallium-67 is 0.015mg and after 13 days the amount of final amount is calculated as follows,

lnA/A0=kt

lnA=-kt+lnA0lnA/A0=-(8

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