If an iron-59 sample has an initial activity of 160 dpm,how much time is required for the activity to drop to 20 dpm? (t1/2 = 45 days)

Question

Quizplus · Accepted Answer

First, we need to determine the decay constant (λ) using the half-life equation:
t1/2 = ln(2)/λ
45 days = ln(2)/λ
λ = ln(2)/45 days = 0.0154 d-1

Next, we use the radioactive decay law equation to solve for time (t):
N(t) = N0 e^(-λt)
where N(t) is the activity at time t, N0 is the initial activity, and e is Euler's constant (approximately 2.71828).

We want to find the time it takes for the activity to drop to 20 dpm, so we set N(t) = 20 dpm and solve for t:
20 dpm = 160 dpm e^(-0.0154 d-1 t)
e^(-0.0154 d-1 t) = 0.125
-0.0154 d-1 t = ln(0.125) = -2.0794
t = 134.9 days

Therefore, the best choice is C) 135 days, which is the closest option to our calculated value.

If an Iron-59 Sample Has an Initial Activity of 160