Physics - Modern Physics Question with Solution | TestHub

Given half-life $T_{1/2}=30$ min and total time $t=90$ min.

Number of half-lives $n=\frac{t}{T_{1/2}}=\frac{90}{30}=3$.

The fraction of radioactive element remaining undecayed is given by $\frac{N}{N_0}={\left(\frac{1}{2}\right)}^n$.

Substituting $n=3$, we get $\frac{N}{N_0}={\left(\frac{1}{2}\right)}^3=\frac{1}{8}$.

Answer: $\frac{1}{8}$