Two radioactive substances X and Y


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:

  1. (1) $\frac{8}{1}$

  2. (2) $\frac{1}{8}$

  3. (3) $\frac{3}{1}$

  4. (4) $\frac{1}{3}$

Correct Option: 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 $\left.3 \mathrm{~T}_{\frac{1}{2} \mathrm{y}}\right)$



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