Nuclei - Result Question 67

68. 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

[2011]

(a) 150 years

(b) 200 years

(c) 250 years

(d) 100 years

Show Answer

Answer:

Correct Answer: 68. (b)

Solution:

  1. (b) Let number of atoms in $X=N_x$

Number of atoms in $Y=N_y$

By question

$\frac{N_x}{N_y}=\frac{1}{15}$

$\therefore$ Part of $N_x=\frac{1}{16}(N_x+N_y)$

$=\frac{1}{2^{4}}(N_x+N_y)$

So, total 4 half lives are passed, so, age of rock is $4 \times 50=200$ years