Question

# What is the mass of $^{60} \mathrm{Co}$ in a cancer therapy transillumination unit containing 5.00 kCi of $^{60} \mathrm{Co} ?$

Solution

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5Here we calculate what is the mass of ${ }^{60} \mathrm{Co}$ used in cancer therapy. The ${ }^{60} \mathrm{Co}$ has the activity of 5kCI and consulting the Appendix in the book we can see it has a half-life of 5.271 years, which is $1.66 \times 10^{8}$ s. So, to calculate the mass of this element, firstly we need to remember the definition of activity:

$R=\frac{0.693 N}{t_{1 / 2}}$

where $N$ is exactly the number of the atoms which will enable us to calculate the mass of the element.

First, we should remember the relation of radioactivity units of Curie and Becquerel, which is: $1 \mathrm{~Bq}=2.70 \times 10^{-11} \ \mathrm{Ci}$.

Following this, now we can convert $5 \mathrm{kCi}$ to Becquerels, so we have:

$\frac{5 \times 10^{3} \ \mathrm{Ci}}{2.70 \times 10^{-11}} = 1.85 \times 10^{14}\ \mathrm{Bq}$

Now expressing the number of the atoms from the first equation we got:

$N=\frac{R\left(t_{1 / 2}\right)}{0.693}$

Putting in all of the numbers:

$N=\frac{1.85 \times 10^{14} \ \mathrm{Bq}\left(1.66 \times 10^{8} \ \mathrm{s}\right)}{0.693}$

We get the result of:

$N=4.44 \times 10^{22}$

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