The thallium subscript 81 superscript 208 baseline tl nucleus is radioactive, with a half-life of 3.053 min. at a given instant, the activity of a certain sample of thallium is 2400 bq. using the concept of a half-life, and without doing any written calculations, determine what the activity 9 minutes later is.
(a) 150 bq
(b) 2400 bq
(c) 1200 bq
(d) 600 bq
(e) 300 bq

(E) 300 bq

Explanation:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

Radioactive decay process is a type of process in which a less stable nuclei decomposes to a stable nuclei by releasing some radiations or particles like alpha, beta particles or gamma-radiations. The radioactive decay follows first order kinetics.

Half life is represented by

Half life of Thallium-208 = 3.053 min

Thus after 9 minutes , three half lives will be passed, after ist half life, the activity would be reduced to half of original i.e. , after second  half life, the activity would be reduced to half of 1200 i.e. ,  and after third half life, the activity would be reduced to half of 600 i.e. ,

Thus the activity 9 minutes later is 300 bq.