Physics - Modern Physics Question with Solution | TestHub

Given that, the initial amount of radium

$N_0=1\mathrm{ mg}$

and number of atoms in 1 mg radium$=2.68\times {10}^8$atoms

$T_{1/2}=1620$years

Number of half-lives

$n=\frac{T}{T_{1/2}}$

$=\frac{3240}{1620}$

$n=2$

$\therefore$Amount after 3240 years

$N=N_0{\left(\frac{1}{2}\right)}^n$

$=1{\left(\frac{1}{2}\right)}^2$

$N=\frac{1}{4}\mathrm{ mg}$

$N=\frac{1}{4}\times 2.68\times {10}^8$atoms

$=0.67\times {10}^8$atoms

$\therefore$Number of disintegrate atoms

$=2.68\times {10}^8-0.67\times {10}^8$

$=2.01\times {10}^8$