Problema Solution
After the release of radioactive material into the atmosphere from a nuclear power plant in a country in 1996, the hay in that country was contaminated by a radioactive isotope (half-life 6 days). If it is safe to feed the hay to cows when 12% of the radioactive isotope remains, how long did the farmers need to wait to use this hay?
Answer provided by our tutors
M = computed mass
M0 = initial mass
T = time
H = half life
Use the equation:
M = M0 * (1/2)^(T/H)
In this case, M = 0.12M0, H = 6 days
0.12M0 = M0 * (1/2)^(T/6)
M0 * (1/2)^(T/6) = 0.12M0
(1/2)^(T/6) = 0.12
T/6 = ln(0.12/0/5)
T = 6ln(0.12)/ln(0.5)
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click here to see the equation solved for T
........
T = 18.35 days
The farmers need to wait 18.35 days.