Question

A tracer study drug contains 10 kBq of 99mTc which has a half-life of 363 minutes. Technetium can be used as a substitute for 131I in tracer studies of the thyroid gland. What is the activity of the drug 3 hours after it was administered?

Answer 1

Let the initial activity of the mTc is A₀ = 10 k Bq = 10⁴ Bq

Half life of the sample is  T_1/2 = 363 min = 21780 s

Disintegration constant = 0.693 / T_1/2

Time after which activity needs to be calculated t = 3 hours

Time t = 10,800 s

Activity of a simple after a time t is given by

A = A₀ e^-t

= A₀ * { e^{-t * (0.693 /} T_1/2⁾ }

= 10⁴ * { e^{-(10800 * 0.693 / 21780 )} }

= 10⁴ * e^-0.3436

= 10⁴ * 0.709

= 7.09 * 10³ Bq

= 7.09 k Bq

So the activity reduces to 7.09 kBq in 3 hours