Iodine-131, t1/2 = 8.0 days, is used in diagnosis and treatment of thyroid gland diseases. if a laboratory sample of iodine-131 initially emits 9.95 × 1018 β particles per day, how long will it take for the activity to drop to 6.22 × 1017 β particles per day?

Explanation:

Formula for the first order decay is as follows.

          = -kt

where,    A = activity at time t

          = initial activity

                k = decay constant

Hence, putting the given values into the above formula as follows.

                 k =

                    =

                    = 0.086643 per day

Also,    

                        t = 32 days

Thus, we can conclude that it will take 32 days for the activity to drop to particles per day.

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