Two radioactive substances X and Y originally have N₁ and N₂ nuclei respectively. Half life of X is half of the life of Y. After three half lives of Y, number of nuclei of both are equal.

The ratio  $\frac{N_1}{N_2}$  will be equal to:

N = N₀e^–λt

->t = λN = N₀/e

So number of nuclei decayed = N₀ – N

= N₀ (1- 1/e) 

Density of nuclei is order of 10¹⁷ kg m^–3.

Density of nuclei is order of 10¹⁷ kg m^-3.

According to Nuclear activity, we can write

$N_0\stackrel{t_{\frac{1}{2}}}{\to }\frac{N_0}{2}\stackrel{t_{\frac{1}{2}}}{\to }\frac{N_0}{4}\stackrel{t_{\frac{1}{2}}}{\to }\frac{N_0}{8}\stackrel{t_{\frac{1}{2}}}{\to }\frac{N_0}{16}=\left(0.0625\right)N_0$         

Time required = 4 × $t_{\frac{1}{2}}=20yrs$