Question

Iodine-131 is used medically to study the activity of the thyroid gland. Iodine – 131 has a half-life of about 8 days. This means that approximately every 8 days, half the mass of the iodine decays into another element. If a container held a mass of 64 milligrams of iodine – 131, how much is left after 40 days?

Answer 1

0.002 mg of sample will be left after 40 days.

Explanation:

Half life of the iodine-131 =
`t_{(1)/(2)}`= 8 days

Initial amount of iodine-131 =
`N_o`= 64 milligrams = 0.064 g

Amount of iodine-131 left after the time of 40 days = N

Decay constant =
`\lambda` = ?

`\lambda =\frac{0.693}{t_{(1)/(2)}}=0.0866 day ^(-1)`

`\log[N]=\log[N_o]-(\lambda * t)/(2.303)`

`\log[N]=\log[0.064 g]-(0.0866 day^(-1)* 40 days)/(2.303)`

`N=Antilog [-2.6979 g]`

N = 0.002004 g = 0.002 mg

0.002 mg of sample will be left after 40 days.