Two elements $P$ and $Q$ have the half-life of $10$ and $15$ minutes respectively. Freshly prepared samples of each isotope initially contain the same number of atoms as each other. After $30$ minutes, the ratio $\frac{n u m b e r o f P a t o m s}{n u m b e r o f Q a t o m s}$ will be____________.

0.5

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Solution

The correct option is A $0.5$
In $30$ minutes, there will be $3$ half life of $P$ and $2$ half lives of $Q$ .
$∴$ Number of $P$ atoms will be $1 / 8$ th and number of $Q$ atoms will be $1 / 4$ th of original atoms.
Then, $\frac{N u m b e r o f a t o m s o f P}{N u m b e r o f a t o m s o f Q} = \frac{1 / 8}{1 / 4} = \frac{1}{2}$ , i.e., $0.5$

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