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 $Tl-201$?$(5.3,5.4)$

Short answer

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

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

Step-by-step solution

    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 $4.0\mathrm{\mu Ci}$.

    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.

   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 $Tl-201=3.0days$.

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