Radioactive decay follows exponential law with half-life

Steps:

• Initial count rate is 4000 cpm, final is 500 cpm after 72 minutes.
• Ratio of initial to final: 4000 / 500 = 8, which equals 2^3, so 3 half-lives occur.
• Half-life T = total time / number of half-lives = 72 min / 3 = 24 min.

Why D is correct:

• Half-life is time for activity to halve; here, activity drops to 1/8 (three halvings) in 72 min, so T = 72 / 3 = 24 min per the decay formula A = A0 (1/2)^{t/T}.

Why the others are wrong:

• A: 8 min implies 9 half-lives in 72 min, reducing to 1/512 of initial (far below 500 cpm).
• B: 9 min implies 8 half-lives, reducing to 1/256 (still too low).
• C: 18 min implies 4 half-lives, reducing to 1/16 or 250 cpm (less than actual 500 cpm).

Final answer: D