Chapter 25, Problem 11STP

Interpretation Introduction

Interpretation:

Estimating the percentage of remaining radioisotope.

Concept introduction:

The period it takes for one-half of a radioactive isotope to decay is known as the half-life.

Answer to Problem 11STP

  $\text{75\%}$

Explanation of Solution

In this problem, 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, the radioisotope remaining in $\text{\%}$ is given. $\text{\%}$

We need to determine the percentage of remaining radioisotope after $\text{0}{\text{.5 t}}_{\text{1}/\text{2}}$ .

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

After 0.5 half-lives, we will have 50% more than after one half-life which is $\text{0}\text{.5×50\%=25\%}$ that is not decayed. In conclusion, $\text{0}{\text{.5 t}}_{\text{1}/\text{2}}$ we will have $\text{50\%+25\%=75\%}$ of remaining radioisotope.

This value can be confirmed if we simply find $\text{0}{\text{.5 t}}_{\text{1}/\text{2}}$ on the x-axis and find the correspondent value on the y-axis which is also $\text{75\%}$ approximately.