$A$ radioactive substance has a half-life of $60 \text{ minutes}$. During $3 \text{ hours}$,the amount of substance decayed would be: (in $\%$)

Two radioactive substances $X$ and $Y$ originally have $N_{1}$ and $N_{2}$ nuclei respectively. The half-life of $X$ is half of the half-life of $Y$. After three half-lives of $Y$,the number of nuclei of both are equal. The ratio $\frac{N_{1}}{N_{2}}$ will be equal to:

The counting rate observed from a radioactive source at $t = 0$ was $1600 \ counts \ s^{-1}$,and at $t = 8 \ s$,it was $100 \ counts \ s^{-1}$. The counting rate observed as $counts \ s^{-1}$ at $t = 6 \ s$ will be

Define the average life of a radioactive substance.

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 $t = 5\, \text{minutes}$. The time (in minutes) at which the activity reduces to half of its initial value is

The half-life of a radioactive isotope $X$ is $50$ years. It decays to another element $Y$ which is stable. The two elements $X$ and $Y$ were found to be in the ratio of $1 : 15$ in a sample of a given rock. The age of the rock was estimated to be..........$years$.