Question

Iodine-131 is one of the many radioactive isotopes resulting from nuclear bomb explosions. how long would it take for 99% of the iodine-131 produced a nuclear explosion to dissappear? the half life of iodine-131 is 8.02 days

Answer 1

For radioactive decay N = N0*e-λt , where N is the number of non-decayed atoms present at time t, N0 is number of atoms present when t = 0 and λ decay constant.

N / N0 = e-λt ...................(1)

The time taken for the radioactivity of a isotope to fall to half its original value is know as half-life of that isotope.

The half life of iodine-131 is 8.02 days. Therefore N / N0 = 0.5 and t = t1/2 = 8.02 days. Putting these values in (1), we get 0.5 =  e-λ​​​​​​​*8.02​​​​​​​ ,Taking ln both side, we get ⟹ ln(0.5) = -λ​​​​​​​*8.02​​​ ...................(2)

For 99% decay of iodine-131 N / N0 = 0.01 and t = t    Putting these values in (1), we get 0.01 =  e-λ​​​​​​​*t ,Taking ln both side, we get ⟹ ln(0.01) = -λ​​​​​​​*t ​​​ ...................(3)

On dividing (3) with (2), we get t = 8.02* ln (0.01) / ln(0.5) = 53.2837 days.

Note - ln means loge.