7.5 Half-life and activity  (Page 5/16)

What mass of ${}^{\text{137}}\text{Cs}$ Escaped chernobyl?

It is estimated that the Chernobyl disaster released 6.0 MCi of ${}^{\text{137}}\text{Cs}$ into the environment. Calculate the mass of ${}^{\text{137}}\text{Cs}$ released.

Strategy

We can calculate the mass released using Avogadro’s number and the concept of a mole if we can first find the number of nuclei $N$ released. Since the activity $R$ is given, and the half-life of ${}^{\text{137}}\text{Cs}$ is found in Appendix B to be 30.2 y, we can use the equation $R=\frac{0\text{.}\text{693}N}{t_{1/2}}$ to find $N$ .

Solution

Solving the equation $R=\frac{0\text{.}\text{693}N}{t_{1/2}}$ for $N$ gives

Entering the given values yields

Converting curies to becquerels and years to seconds, we get

One mole of a nuclide ${}^{A}X$ has a mass of $A$ grams, so that one mole of ${}^{\text{137}}\text{Cs}$ has a mass of 137 g. A mole has $6\text{.}\text{02}\times {\text{10}}^{\text{23}}$ nuclei. Thus the mass of ${}^{\text{137}}\text{Cs}$ released was

Discussion

While 70 kg of material may not be a very large mass compared to the amount of fuel in a power plant, it is extremely radioactive, since it only has a 30-year half-life. Six megacuries (6.0 MCi) is an extraordinary amount of activity but is only a fraction of what is produced in nuclear reactors. Similar amounts of the other isotopes were also released at Chernobyl. Although the chances of such a disaster may have seemed small, the consequences were extremely severe, requiring greater caution than was used. More will be said about safe reactor design in the next chapter, but it should be noted that Western reactors have a fundamentally safer design.