Physics - Modern Physics Question with Solution | TestHub

Fraction of the sample decayed is $\frac{7}{8}$.

Fraction of the sample remaining is $1-\frac{7}{8}=\frac{1}{8}$.

The amount of substance remaining after time $t$ is given by $N=N_0{\left(\frac{1}{2}\right)}^{\frac{t}{T_{1/2}}}$.

Substituting the values, we get $\frac{1}{8}={\left(\frac{1}{2}\right)}^{\frac{t}{15}}$.

${\left(\frac{1}{2}\right)}^3={\left(\frac{1}{2}\right)}^{\frac{t}{15}}$

$\frac{t}{15}=3$

$t=45$ hr.

Answer: $45$ hour