Question

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

Answer 1

The correct option is C 200 years

As $\frac{N_X}{N_Y}=\frac{1}{15},N_X+N_Y=16N_X$
Thus, $\frac{N_X}{N_X+N_Y}=\frac{1}{16}$
or $N_X=\frac{1}{16}(N_X+N_Y)=\frac{1}{2^4}(N_X+N_Y)$
Age of the rock = number of half -lives of isotope
X years passed = $4=4\times 50years=200years$