Question

The half-life of a radioactive isotope ‘X’ is 20 years. It decays to another element ‘Y’ which is stable. The two elements ‘X’ and ‘Y’ were found to be in the ratio 1 : 7 in a sample of a given rock. The age of the rock is estimated to be -

• A. 40 years
• B. 60 years
• C. 80 years
• D. 100 years

Answer 1

The correct option is B 60 years

Half-life of X $\Rightarrow T_X$ = 20 years

$\frac{N}{N_0}=\frac{1}{1+7}=\frac{1}{8}=\frac{1}{2^n}=\frac{1}{2^3}n=3=\frac{1}{T}=\frac{1}{20}$
t = 60 years