Two radioactive isotopes P and Q have half-li | vedclass

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(A) Given,half-life of $P$,$T_P = 10 	ext{ min}$ and half-life of $Q$,$T_Q = 15 	ext{ min}$.Initially,both samples have the same number of atoms,$N_

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$0.5$

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(A) Given,half-life of $P$,$T_P = 10 	ext{ min}$ and half-life of $Q$,$T_Q = 15 	ext{ min}$.Initially,both samples have the same number of atoms,$N_0$.After time $t = 30 	ext{ min}$,the number of half-lives for $P$ is $n_P = \frac{t}{T_P} = \frac{30}{10} = 3$.The number of half-lives for $Q$ is $n_Q = \frac{t}{T_Q} = \frac{30}{15} = 2$.The remaining number of atoms for $P$ is $N_P = N_0 \left(\frac{1}{2}ight)^{n_P} = N_0 \left(\frac{1}{2}ight)^3 = \frac{N_0}{8}$.The remaining number of atoms for $Q$ is $N_Q = N_0 \left(\frac{1}{2}ight)^{n_Q} = N_0 \left(\frac{1}{2}ight)^2 = \frac{N_0}{4}$.The ratio $\frac{N_P}{N_Q} = \frac{N_0/8}{N_0/4} = \frac{4}{8} = 0.5$.

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