Question

 

Iridium-192 is one radioisotope used in brachytherapy, in which a radioactive source is placed inside a patient's body to treat cancer. Brachytherapy allows the use of a higher than normal dose to be placed near the tumor while lowering the risk of damage to healthy tissue. Iridium-192 is often used in the head or breast.

 

 

Answer the following three questions (a, b, and c) based on the radioactive decay curve of iridium-192, shown below. Click on the graph and move the mouse over a point to get values for that point.

 

If the initial sample is 5.25 g. what mass of the original iridium-192 remains after 130 days?

Estimate the half-life of the radioisotope.

How many days would it take for two-thirds of the sample to decay?

 

You must understand the graph to answer this question. The x axis represents the time in days, and the y axis shows the sample remaining after x days. For example, about 63% of the sample remains after 50 days.

Consider the percent of the original sample that remains after 130 days.

The half-life is the amount of time that it takes for one-half of the radioactive material to decay.

Think about the amount of sample left after two-thirds of the material decays.

Answer 1

(a) From the graph, the percentage of the sample after 130 days is \(30 \%\)

The mass of the initial sample is \(5.25 \mathrm{~g}\).

So, calculate the mass of original iridium-192 after 130 days as follows:

mass of original \(=30 \% \times\) mass of the initial sample

$$ \begin{aligned} &=\frac{30}{100} \times(5.25 \mathrm{~g}) \\ &=1.575 \mathrm{~g} \\ &\cong 1.58 \mathrm{~g} \end{aligned} $$

(b) From the graph, the half-life at \(50 \%\) sample is about 75 days.

(c) Two-third of the sample decay means one-third remains, that is \(33 \%\). Then time is 120 days from graph.