A radioactive element X converts into another stable element Y. Half life of X is 2 hours. Initially only X is present. After time t the ratio of atoms of X and Y is found to be 1 : 7, then t in hours is
Answer & explanation
Correct answer: option 3
$\text{Let initial number of nuclei is }N_0$
$ \text{After time t let number of nuclei of X is N}$
$ \Rightarrow N_0 = N + 7N = 8N$
$\Rightarrow N = \frac{N_0}{8}$
$ \frac{N_0}{8} = \frac{N_0}{2^n}$
$ n = \frac{t}{t_{1/2}} = 3$
$ t = 3t_{1/2} = 6hours $