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Q.
A radioactive sample contains $10^{-3}\,kg$ each of two nuclear species $A$ and $B$ with half-life $4\, days$ and $8\, days$ respectively. The ratio of the amounts of $A$ and $B$ after a period of $16\, days$ is
Given, half- life of species $A=4$ days
Half- life of species $B=8$ days
For species $A, N=N_{0}\left(\frac{1}{2}\right)^{n} ; n=\frac{16}{4}=4$
Now, $N_{1}=N_{0}\left(\frac{1}{2}\right)^{4}$ ...(i)
Similarly, for species $B$
$N_{2}=N_{0}\left(\frac{1}{2}\right)^{2}$ ...(ii)
On dividing Eq. (i) from Eq. (ii), we get
$\frac{N_{1}}{N_{2}} =\frac{(2)^{2}}{(2)^{4}}$
$\Rightarrow \frac{N_{1}}{N_{2}}=\frac{1}{4}$
$\Rightarrow N_{1}: N_{2} =1: 4$