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1. The Chernobyl nuclear explosion in the former Soviet Union on April 26, 1986 released large amounts of radioactive substances into the atmosphere. These substances included cesium-137, iodine-131, and strontium-90. Although the radioactive material covered many countries, the actual amount and intensity of the fallout varied greatly from country to country, due to vagaries of the weather and the winds. One area that was particularly hard hit was Lapland, where heavy rainfall occurred just when the Chernobyl cloud was overhead.
a) Many of the pastures in Lapland were contaminated with cesium-137, a radioactive substance
with a half-life of 33 years. If the amount of cesium-137 was found to be ten times the normal
level, how long would it take until the level returned to normal? (Hint: Let No be the amount
that is ten times the normal level. Then you want to find the time when N(t) = No/10.)
b) Assume that the amount of cesium-137 was 100 times the normal level, how long would it take
until the level returned to normal? (Remark: Several days after the explosion, it was reported
that the level of cesium-137 in the air over Sweden was 10,000 times the normal level.
Fortunately there was little or no rainfall.)
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