Question

Review Constants Periodic a substance active times that the countable and will therefore decay by my name of processes the decay Del decay of the day of radioactive comm o der Therefore theme of daycan t orbed by the megrated w omen e n we used to describe the food chemical con In where the mo s t coloraty t he com by man of these quo ng 0. the world when contre long for fraction remaining - - (0.5)" P o w er 400 counted Express your answer with the appropriate units Where is the number of harves. The chaves lots store menumber

Answer 1

Since the radioactive decay follows first order decay,

At = Ao exp (-kt),    where k is the rate constant.

Initial activity, Ao = 400 counts

activity at 36.7 min , At = 100 counts , at t = 36.7 min

Using the above equation,

100 = 400 exp (-k x 36.7 min)

Or, exp (-k x 36.7 min) = (1/4)

Taking ln on both sides

- k (36.7 min) = ln (1/4) = -ln 4

So, k = {ln 4 / (36.7) } min-1 = 0.0378 min-1

So, half-life: t1/2 = 0.693 / k

    putting values:    t1/2 = (0.693 / 0.0378) min = 18.3 min

Hence half -life is 18. 3 min