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)

........

click here to see the equation solved for T

........

T = 18.35 days

The farmers need to wait 18.35 days.