The half-life of a radioactive sample is $20 \ days$. This means that:

At $t = 0$,the counting rate from a radioactive source is $1600 \text{ counts/s}$,and at $t = 8 \text{ s}$,it is $100 \text{ counts/s}$. The counting rate at $t = 6 \text{ s}$ will be:

Two radioactive materials $M_1$ and $M_2$ have decay constants $9 \lambda$ and $\lambda$ respectively. Initially,they have the same number of nuclei. The ratio of the number of nuclei of $M_1$ to that of $M_2$ will be $\frac{1}{e}$ after a time interval of:

Consider a radioactive material of half-life $1.0 \, \text{minute}$. If one of the nuclei decays now,the next one will decay

Two radioactive samples $A_1$ and $A_2$ have decay constants $10\lambda_0$ and $\lambda_0$ respectively. If they initially contain the same number of nuclei,find the ratio of the number of undecayed nuclei after time $t = 1/(9\lambda_0)$.

The percentage of ${}^{235}U$ presently on Earth is $0.72\%$ and the rest $(99.28\%)$ may be taken to be ${}^{238}U$. Assume that all uranium on Earth was produced in a supernova explosion long ago with the initial ratio ${}^{235}U / {}^{238}U = 2.0$. How long ago did the supernova event occur? (Take the half-lives of ${}^{235}U$ and ${}^{238}U$ to be $7.1 \times 10^8$ years and $4.5 \times 10^9$ years respectively).