Q: The radioactive isotope X with a half life of 10^{9} years decays to Y which is stable. A sample of rocks was found to contain both the elements X and Y in the radio 1∶ 7. What is the age of the rocks ?

(a) 2 × 10^{9} Y

(b) 3 × 10^{9} Y

(c) 6 × 10^{9} Y

(d) 7 × 10^{9} Y

Ans: (b)

Sol: $ \displaystyle \frac{N}{N_0} = \frac{1}{1+7} $

$ \displaystyle \frac{N}{N_0} = \frac{1}{8} = (\frac{1}{2})^3$

As we know , $ \displaystyle \frac{N}{N_0} = (\frac{1}{2})^n $

On comparing we get,

n= 3

t = n T

= 3 × 10^{9} Y