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 of 1: 7 in a sample of a the given rock. The age of the rock is estimated to be

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 of 1: 7 in a sample of a the given rock. The age of the rock is estimated to be (A) 60 years (B) 80 years (C) 100 years (D) 40 years

Tardigrade Admin · Accepted Answer

The value of X is (1/8) =( x 0/8)=( x 0/23) ⇒ t =3 T =3 × 20=60 years Hence the estimated age of the rock is 60 years

Q. 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 of $1 : 7$ in a sample of a the given rock. The age of the rock is estimated to be

60 years

80 years

100 years

40 years

The value of $X$ is $\frac{1}{8}$
$= \frac{x _{0}}{8} = \frac{x _{0}}{2 ^{3}}$
$\Rightarrow t = 3 T = 3 \times 20 = 60$ years
Hence the estimated age of the rock is $60$ years

Q. 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 of 1:7 in a sample of a the given rock. The age of the rock is estimated to be