Question

Iodine-131, t1/2 = 8.0 days, is used in the diagnosis and treatment of thyroid gland diseases. If a laboratory sample of iodine-131 initially emits 9.95 × 1018 β particles per day, how long will it take for the activity to drop to 6.22 × 1017 β particles per day?

Answer 1

Answer:

32,0 days.

Explanation:

The radioactive decay follows:

$N_{t} = N_{0}e^{\frac{-0.693t}{t_{1/2}}$

Where Nt is the concentration in a time t (6,22x10¹⁷), N₀ is the initial concentration (9,95x10¹⁸) Half life time is 8,0 days and t is the time it take to drop this concentration. Replacing:

$6.22x10^{17} = 9,95x10^{18}e^{\frac{-0.693t}{8 days}$

$0,0625 = e^{\frac{-0.693t}{8days}$

$ln 0,0625 = {\frac{-0.693t}{8days}$

$-2,77*8days = -0.693t$

$-22,2days = -0.693t$

$32,0days = t$

It take 32,0 days

I hope it helps!