After the release of radioactive material into the atmosphere from a nuclear pow
ID: 2868225 • Letter: A
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). If it is safe to feed the hay to cows when 10% of the iodine 131 remains, how long did the farmers need to wait to use this hay? 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). If it is safe to feed the hay to cows when 10% of the iodine 131 remains, how long did the farmers need to wait to use this hay? 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). If it is safe to feed the hay to cows when 10% of the iodine 131 remains, how long did the farmers need to wait to use this hay?Explanation / Answer
M = computed mass
M0 = initial mass
T = time
H = half life
Use the equation:
M = M0 * (1/2)^(T/H)
In this case, our masses will simply be
percentages, but that's OK as long as
both sides of the equation are consistent.
0.10 = 1.0 * (1/2)^(T/8)
0.10 = (1/2)^(T/8)
ln(0.10) = ln((1/2)^(T/8))
ln(0.10) = (T/8) * ln((1/2))
ln(0.10) / ln(1/2) = (T/8)
8 ( ln(0.10) / ln(1/2) ) = T
26.5754 = T
Therefore, rounding to an even number of days,
the farmers would need to wait 27 days.
As a sanity check,
After 8 days, 1/2 of iodine is radioactive
After 16 days, 1/4 is radioactive
After 24 days, 1/8 is radioactive
After 32 days, 1/16 is radioactive
So we can see that it would take a little more
than 24 days (and quite a bit less than 32 days)
to get to a 10% level of iodine. Thus, the
computed result of 26.57 days looks reasonable.