Question

A 256- gallon barrel of radioactive Urikium is spilled at a factory. The entire area is evacuated. Experts say that the area can be deemed safe after only 2 gallons remain. Unfortunately, it is to toxic for any clean-up efforts, so residents will just have to wait for the Urikium to evaporate. Fortunately, Urikium has a half-life of only three hours. That means that half of the Urikium will evaporate every three hours

Answer 1

Experts say that the area can be deemed safe after only 2 gallons remain. Unfortunately, it is too toxic for any clean-up efforts. She residents will

Explanation:

To solve half-life problems, you use the equations:

f(t) = T0 (1/2)^(t/t1/2). where T0 is the initial mass and T1/2 is the half-life.

So we get f(20)= 5 = T0•(1/2) ^ 20/11

T0 = 17.63 mg

For the second part of the question, we plug 0.5 mg into the equation:

0.5 = 17.63 • (1/2)^ t/11

t = 56.5 days

Answer 2

21 hours

Explanation:

Since 2^8 = 256, that means it will take 7 half-lives to become two gallons

7 half-lives * 3 hours = 21 hours

256, 128, 64, 32, 16, 8, 4, 2