$A$ radioactive element has a half-life of $15$ years. What is the fraction that will decay in $30$ years?

The half-life of a radioactive substance is $20 \ min$. The time interval between $20\%$ decay and $80\%$ decay is ......... $min$.

In an old rock,the ratio of uranium to lead nuclei is $1:1$. The half-life of uranium is $4.5 \times 10^9$ years. If the rock initially contained only uranium nuclei,how old is the rock?

In a radioactive sample,there are $1.414 \times 10^6$ active nuclei. If they reduce to $10^6$ within $10 \text{ min}$,then the half-life of this sample will be ....... $\text{min}$.

The decay constant of radium is $4.28 \times 10^{-4}$ per year. Its half-life will be .......... $years$.

The activity of a radioactive sample is measured as $N_0$ counts per minute at $t = 0$ and $N_0/e$ counts per minute at $t = 5$ minutes. The time (in minutes) at which the activity reduces to half of its initial value is