Question

The unstable iodine isotope 53 I (half-life: 8.03 days) is often given to cats with 131 hyperthyroidism. The cats then eliminate the radioactive material into their litterboxes (one hopes). If the initial activity of the litterbox is 10 times the safe level for human handling, how long must you wait before it's safe to throw the litter into the trash?

Answer 1

Half-life of unstable iodine isotope 53 I = T_1/2 = 8.03 days

Decay constant =

= 8.632 x 10^-2 days^-1

Safe level of activity of the iodine isotope for human handling = N

Initial activity of the litter box = N₀ = 10N

Time period you must wait before it's safe to throw the litter into the trash = T

Taking natural log on both sides,

T = 26.67 days

Time period you must wait before it's safe to throw the litter into the trash = 26.67 days