1. Tardigrade
  2. Question
  3. Physics
  4. A radioactive sample of half-life 10 days, contains 1000x nuclei. Number of original nuclei present after 5 days is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. A radioactive sample of half-life $10$ days, contains $1000x$ nuclei. Number of original nuclei present after $5$ days is

NTA AbhyasNTA Abhyas 2020Nuclei

Solution:

The number of radioactive nuclei left after n half lives is
$N=\frac{N_{0}}{2^{n}}$

$for 5 days n=\frac{1}{2}$
So, $N=\frac{1000 x}{2^{\frac{1}{2}}}=\frac{1000 x}{\sqrt{2}}$
$=\frac{1000 x}{1.414}=\left(0.707\right)1000x$
$=707x$