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

Answer:

0.002 mg of sample will be left after 40 days.

Step-by-step explanation:

Half life of the iodine-131 =$t_{\frac{1}{2}}$= 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 =$\lambda$ = ?

$\lambda =\frac{0.693}{t_{\frac{1}{2}}}=0.0866 day ^{-1}$

$\log[N]=\log[N_o]-\frac{\lambda \times t}{2.303}$

$\log[N]=\log[0.064 g]-\frac{0.0866 day^{-1}\times 40 days}{2.303}$

$N=Antilog [-2.6979 g]$

N = 0.002004 g = 0.002 mg

0.002 mg of sample will be left after 40 days.