Two radioactive isotopes P and Q have half Jives 10 minutes and 15 minutes respectively. Freshly pre

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13.Nuclei

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Two radioactive isotopes $P$ and $Q$ have half Jives $10$ minutes and $15$ minutes respectively. Freshly prepared samples of each isotope initially gontain the same number of atoms. After $30$ minutes, the ratio $\frac{\text { number of atoms of } P}{\text { number of atoms of } Q}$ will be

A

$0.5$

B

$2.0$

C

$1.0$

D

$3.0$

Solution

(a)

$T_P=10$ minute $\quad T_Q=15$ minute

After $30$ minute $P$ has gone $3$ half lives and $Q=2$ half lives

$N_P=N_0\left(\frac{1}{2}\right)^3$ $\quad N_Q=N_0\left(\frac{1}{2}\right)^2$

$N_P: N_Q=1: 2$

$\text { or } \frac{N_P}{N_Q}=0.5$

Standard 12

Physics

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