Question

An unknown amount of iodine-131 sample was placed in a container, and 50.0 mg is

remaining 32.4 days later. If its half-life is 8.1 days, how many milligrams of iodine-131 was originally placed in a container (32.4 days ago)?

Answer 1

We can use the half-life formula to solve the problem:

N = N0 * (1/2)^(t/t1/2)

where:
N0 = initial amount
N = remaining amount
t = time elapsed
t1/2 = half-life

We are given:
N0 = unknown
N = 50.0 mg
t1/2 = 8.1 days
t = 32.4 days

Substituting the values, we get:

50.0 = N0 * (1/2)^(32.4/8.1)

50.0 = N0 * 0.1487

N0 = 50.0 / 0.1487

N0 = 336.09 mg (rounded to two decimal places)

Therefore, the original amount of iodine-131 placed in the container was approximately 336.09 mg.