Two radioactive substances $X$ and $Y$ originally have $N_{1}$ and $N_{2}$ nuclei respectively.
Half life of $X$ is half of the half life of $Y$. After there half lives of $Y$, number of nuclei of both are equal. The ratio $\frac{N_{1}}{N_{2}}$ will be equal to:
Correct Option: 1
(1)
After $\mathbf{n}$ half life no of nuclei undecayed $=\frac{N_{o}}{2^{\mathrm{n}}}$
given $\mathrm{T}_{\frac{1}{2} \mathrm{x}}=\frac{\mathrm{T}_{\frac{1}{2} \mathrm{y}}}{2}$
So 3 half life of $y=6$ half life of $x$
Given, $\mathrm{N}_{\mathrm{x}}=\mathrm{N}_{\mathrm{y}}\left(\right.$ after $\left.3 \mathrm{~T}_{\frac{1}{2} \mathrm{y}}\right)$
$\frac{N_{1}}{2^{6}}=\frac{N_{2}}{2^{3}}$
$\frac{N_{1}}{N_{2}}=\frac{2^{6}}{2^{3}}=2^{3}=\frac{8}{1}$
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