Question

After the release of radioactive material into the atmosphere from a nuclear power plant at Chernobyl (Ukraine) in 1986, the hay in Austria was contaminated by iodine 131 (half-life 8 days). It is safe to feed the hay to cows when 10% of the iodine 131 remains.

1. What is the exact growth/decay factor?
2. How long did the farmers need to wait to use this hay?

Answer 1

The growth/decay factor for iodine-131 with an 8-day half-life is 0.5. Using logarithms, it can be calculated that farmers need to wait approximately 26.33 days before it's safe to feed the contaminated hay to cows, at which point the iodine level is reduced to 10%.

Step-by-step explanation:

The exact growth/decay factor for iodine-131, with a half-life of 8 days, is calculated using the formula for exponential decay, which is:

N(t) = N0(1/2)^(t/h)

Where N(t) is the remaining quantity of substance at time t, N0 is the initial quantity of substance, and h is the half-life of the substance.

To find out when it's safe to feed the hay to cows, we set the remaining amount as 10% of the original, like this:

0.10 = (1/2)^(t/8)

To solve for t, we take the logarithm of both sides of the equation. Using the law of logarithms, we find:

t = 8 * (log(0.10)/log(0.5))

Calculating this, the farmers need to wait approximately 26.33 days before the iodine-131 levels are reduced to 10% of their initial amount and the hay is safe to feed to cows.