Physics - Modern Physics Question with Solution | TestHub

Initial number of atoms, $N_0=8\times 10^{10}$

Half-life, $T_{1/2}=1$ hour

Number of atoms remaining at $t=2$ hours ($n=2$ half-lives):

$N_1=N_0{\left(\frac{1}{2}\right)}^2=\frac{8\times 10^{10}}{4}=2\times 10^{10}$

Number of atoms remaining at $t=5$ hours ($n=5$ half-lives):

$N_2=N_0{\left(\frac{1}{2}\right)}^5=\frac{8\times 10^{10}}{32}=0.25\times 10^{10}$

Number of atoms decayed in the time interval $t=2$ hour to $t=5$ hour:

$\Delta N=N_1-N_2=2\times 10^{10}-0.25\times 10^{10}=1.75\times 10^{10}$

Answer: $1.75\times 10^{10}$