Q. 5.83 - An Introduction to General, Organic, and Biological Chemistry

Question

A $64- \mathrm{\mu Ci}$ sample of $Tl-201$ decays to $4.0\mu \mathrm{Ci}$ in $12$ days. What is the half-life, in days, of $Tl-201$?$(5.3,5.4)$

Step-by-Step Solution

Answer

        As a result, a half-life of $Tl-201=3.0 days.$

The $TI-201$ has a $3.0 days$  half-life.

Step 1: Introduction

Half-life:

      A  half life is the time it takes for half of a radioactive  sample to decay.  .In $12$ days, the $TI-201$ sample drops from $64.0 \mathrm{\mu Ci}$ to $4.0 \mathrm{\mu Ci}.$

Calculate the number of half-lives required to reduce the sample size from $64.0 \mu Ci$ to $4.0 \mathrm{\mu Ci}$.

Step 2: Explanation

$64.0 \mathrm{\mu Ci} \mathrm{TI}-201\stackrel{1 \mathrm{half}-\mathrm{life}}{\to }32.0 \mathrm{\mu Ci} \mathrm{TI}-201\stackrel{2 \mathrm{half}-\mathrm{lives}}{\to }16.0 \mathrm{\mu Ci} \mathrm{TI}-201\stackrel{3 \mathrm{half}-\mathrm{lives}}{\to }8.0 \mathrm{\mu Ci} \mathrm{TI}-201\stackrel{4 \mathrm{half}-\mathrm{lives}}{\to }4.0 \mathrm{\mu Ci} \mathrm{TI}-201$

To reduce the $Tl-201$ sample from $64.0 \mu Ci$ to $4.0 \mu Ci$, four half-lives are required.

Step 3: Conclusion

Calculate the half-life of $TI-201$ as follows:

$4 \mathrm{half} -\mathrm{lives} \mathrm{for}(TI-201)=12 \mathrm{days}$

$1 \mathrm{half}-\mathrm{life} \mathrm{of} TI-201=3.0 \mathrm{days}$

As a result, a half-life of $Tl-201=3.0 days$.

The $TI-201$ has a $3.0$ day half-life.