Question

After the release of radioactive material into the atmosphere from a nuclear power plant in a country in 1980​, 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 14​% of the radioactive isotope​ remains, how long did the farmers need to wait to use this​ hay?

Answer 1

Answer:

30 days

Step by step explanation:

The half-life of the isotope is 6 days, meaning that the amount of the isotope is reduced to half every 6 days.

Let's assume that the initial amount of the isotope in the hay is 100%.

After one half-life (6 days), the amount of the isotope remaining in the hay is 50%.

After two half-lives (12 days), the amount of the isotope remaining in the hay is 25%.

After three half-lives (18 days), the amount of the isotope remaining in the hay is 12.5%.

After four half-lives (24 days), the amount of the isotope remaining in the hay is 6.25%.

After five half-lives (30 days), the amount of the isotope remaining in the hay is 3.125%.

Therefore, the farmers needed to wait for at least 30 days (5 half-lives) until the amount of the radioactive isotope in the hay decreased to 14% or less.

Answer 2

22

Explanation:

The time required for a radioactive isotope to decay to a certain percentage of its initial amount can be found using the following formula:

t = (t1/2 / ln(2)) * ln(N0/N1)

where:

t is the time elapsed since the release of the radioactive material

t1/2 is the half-life of the radioactive isotope (6 days in this case)

N0 is the initial amount of the radioactive isotope

N1 is the remaining amount of the radioactive isotope (14% of N0 in this case)

ln is the natural logarithm

We can solve for t by plugging in the given values:

t = (6 / ln(2)) * ln(1 / 0.14)

t ≈ 22.4 days

Therefore, the farmers needed to wait about 22.4 days to use the hay safely.