Question

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

Answer 1

Answer: (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 $t_{\frac{1}{2}$

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. $\frac{2400}{2}=1200$, after second  half life, the activity would be reduced to half of 1200 i.e. $\frac{1200}{2}=600$,  and after third half life, the activity would be reduced to half of 600 i.e. $\frac{600}{2}=300$,

Thus the activity 9 minutes later is 300 bq.