1. Tardigrade
  2. Question
  3. Physics
  4. Two radioactive isotopes P and Q have half lives 10 minutes and 15 minutes respectively. Freshly prepared samples of each isotope initially contain the same number of atoms. After 30 minutes, the ratio ( textnumber of atoms of P/ textnumber of atoms of Q) will be

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Two radioactive isotopes $P$ and $Q$ have half lives $10$ minutes and $15 $ minutes respectively. Freshly prepared samples of each isotope initially contain 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

Nuclei

Solution:

$T_{p}=10$ minute
$T_{Q}=15$ 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} $
$N_{Q}=N_{0}\left(\frac{1}{2}\right)^{2}$
$N_{P}: N_{Q}=1: 2$
or $\frac{N_{P}}{N_{Q}}=0.5$