Iodine-131, t_1/2= 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?

Question

Quizplus · Accepted Answer

We can use the radioactive decay law to solve for the time it takes for the activity to drop to a certain level:

A(t) = A0*(1/2)^(t/t1/2)

where A(t) is the activity at time t, A0 is the initial activity, t1/2 is the half-life, and t is the time elapsed.

We can rearrange this equation to solve for t:

t = t1/2*(log(A(t)/A0)/log(1/2))

Plugging in the given values, we get:

t = 8.0*(log(6.22E17/9.95E18)/log(1/2)) = 31.9 days

Rounding to the nearest whole number, the answer is C) 32 days.

Iodine-131, T1/2 = 8

Iodine-131, T_1/2= 8