For a radioactive material, the half-life is 10 minutes . If initially there are 600 number of nuclei, the…

Given,

$N_0=600$; $N^{\prime }=450$
$N=N_0-N^{\prime }$
$N=150$
Number of remaining nuclei,
$\frac{N}{N_0}={\left(\frac{1}{2}\right)}^{\frac{t}{t_{1/2}}}$ (Here, when, $t=t_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\Rightarrow N=\frac{N_0}{2}$) 

$\Rightarrow \frac{150}{600}={\left(\frac{1}{2}\right)}^{\frac{t}{10}}$
$\Rightarrow \frac{1}{4}={\left(\frac{1}{2}\right)}^{\frac{t}{10} }\Rightarrow {\left(\frac{1}{2}\right)}^2={\left(\frac{1}{2}\right)}^{\frac{t}{10}}$
$2=\frac{t}{10}\Rightarrow t=20 \mathrm{minutes}$