Question

Cesium-137, which has a half-life of 30.2 , is a component of the radioactive waste from nuclear power plants. If the activity due to cesium-137 in a sample of radioactive waste has decreased to 35.2 of its initial value, how old is the sample?

1.04 yr

15.4 yr

31.5 yr

45.5 yr

156 yr

Answer 1

Since cesium-137 has a half-life of 30.2 years, this means that its activity decreases by half every 30.2 years.

Let t be the time elapsed since the sample was produced. Then, the fraction of cesium-137 remaining in the sample is:

(1/2)^(t/30.2)

We are given that the activity due to cesium-137 in the sample has decreased to 35.2% of its initial value. This means that the remaining fraction of cesium-137 is:

0.352 = (1/2)^(t/30.2)

Taking the logarithm of both sides, we get:

log(0.352) = (t/30.2) log(1/2)

Solving for t, we get:

t = (log(0.352) / log(1/2)) * 30.2
t ≈ 45.5 years

Therefore, the sample is approximately 45.5 years old (option D).