Chapter 24, Problem 56A

Interpretation Introduction

Interpretation:

The remaining amount of 25.0g sample needs to be calculated.

Concept introduction:

The time period that is needed for one-half of a radioisotope’s nuclei to decay into its products is half life.

Answer to Problem 56A

The remaining amount is 4g.

Explanation of Solution

After a given amount of time has elapsed the remaining amount of a radioactive sample is given by the formula is as follows:

${\text{N=N}}_{\text{0}}{\left(\frac{\text{1}}{\text{2}}\right)}^{\frac{\text{t}}{\text{T}}}$

Here N is mass of sample, ${\text{N}}_{\text{0}}$ is original mass, t is the time elapsed and T is duration of samples half life.

Given ${\text{N}}_{\text{0}}=25\text{g}$, T=138 d, t = one year (365 days)

Put these values in above equation is as follows:

$\begin{array}{c}\text{N=25g}\times {\left(\frac{\text{1}}{\text{2}}\right)}^{\frac{365}{138}}\\ =\text{25g}\times {\left(\frac{\text{1}}{\text{2}}\right)}^{2.64}\\ =4\text{g}\end{array}$

Thus mass of the sample is 4g.

Conclusion

The mass of the sample is 4g which is remaining amount.