Chapter 25, Problem 12STP

Interpretation Introduction

Interpretation:

Estimating the percentage of remaining radioisotope.

Concept introduction:

Radioisotopes can be defined as atoms that contain an unstable combination of neutrons and protons, or excess energy in their nucleus.

Answer to Problem 12STP

  $\text{43\%}$

Explanation of Solution

The given graph represents the decay curve for radioactive isotope where on the x-axis number of half-lives is given, and on the y-axis radioisotope remaining in % is given.

We need to determine the percentage of remaining radioisotope after $\text{1}{\text{.25t}}_{\frac{\text{1}}{\text{2}}}$

If we use $\text{100\%}$ of radioisotope initially, after one half-life we will have $\frac{\text{1}}{\text{2}}$ of that percentage $\left(\text{50\%}\right)$ .

After $0.25$ half-lives, we will have an additional $25\%$ from the half nuclei ( $25\%$ ) that will decay which is: $\text{0}\text{.25×25\%=6}\text{.25\%}$ more.

This value represents the additional nuclei that will decay and now we have $\text{50\%-6}\text{.25\%=43}\text{.75\%}$

In conclusion, after $\text{1}{\text{.25t}}_{\frac{\text{1}}{\text{2}}}$ , we will have $\text{43}\text{.75\%}$ of remaining radioisotope.

This value can be confirmed if we simply find $\text{1}{\text{.25t}}_{\frac{\text{1}}{\text{2}}}$ on the x-axis and find the correspondent value on the y-axis which is around $\text{43\%}$