10.7 Medical applications and biological effects of nuclear radiation  (Page 5/18)

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

The Chernobyl accident in Ukraine (formerly in the Soviet Union) exposed the surrounding population to a large amount of radiation through the decay of ${}^{137}\text{Cs}$ . The initial radioactivity level was approximately $A=6.0\text{MCi}.$ Calculate the total mass of ${}^{137}\text{Cs}$ involved in this accident.

Strategy

The total number of nuclei, N , can be determined from the known half-life and activity of ${}^{137}\text{Cs}$ (30.2 y). The mass can be calculated from N using the concept of a mole.

Solution

Solving the equation $A=\frac{0.693N}{t_{1\text{/}2}}$ for N gives

Entering the given values yields

To convert from curies to becquerels and years to seconds, we write

One mole of a nuclide ${}^A\text{X}$ has a mass of A grams, so that one mole of ${}^{137}\text{Cs}$ has a mass of 137 g. A mole has $6.02\times {10}^{23}$ nuclei. Thus the mass of ${}^{137}\text{Cs}$ released was

Significance

The mass of ${}^{137}\text{Cs}$ involved in the Chernobyl accident is a small material compared to the typical amount of fuel used in a nuclear reactor. However, approximately 250 people were admitted to local hospitals immediately after the accident, and diagnosed as suffering acute radiation syndrome. They received external radiation dosages between 1 and 16 Sv. Referring to biological effects in [link] , these dosages are extremely hazardous. The eventual death toll is estimated to be around 4000 people, primarily due to radiation-induced cancer.

Got questions? Get instant answers now!