Q. The half life of a radioactive isotope X is 50 years. It decays to another element Y which is stable. The two elements X and Y were found to be in the ratio of 1 : 15 in a sample of a given rock. The age of the rock was estimated to be
A) 100 years
B) 150 years
C) 200 years
D) 250 years
Explanation
[Solution from source] If X : Y = 1 : 15, the fraction of X remaining is 1/16 = (1/2)⁴, so four half-lives have passed: 4 × 50 = 200 years. Taking 1/15 as the remaining fraction or counting 3 half-lives gives the wrong ages. Answer (3).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.