Using a nuclear counter, the count rate of emitted particles from a radioactive source is measured. At $t = 0$, it was $1600$ counts per second, and at $t = 8 \, s$, it was $100$ counts per second. The count rate observed, in counts per second, at $t = 6 \, s$ is close to:

Two radioactive materials $A$ and $B$ have decay constants $5\lambda$ and $\lambda$ respectively. At $t=0$,they have the same number of nuclei. The ratio of the number of nuclei of $A$ to that of $B$ will be $(1/e)^2$ after a time interval of:

$A$ radioactive material whose half-life period is $2$ years weighs $1 \,g$ and is stored in the laboratory for $4$ years. Then the amount of remaining radioactive material is (in $\,g$)

The half-life of radioactive Radon is $3.8 \ days$. The time at the end of which $1/20^{th}$ of the Radon sample will remain undecayed is ........... $days$ (Given $\log_{10} e = 0.4343$).

Substance $A$ has an atomic mass number of $16$ and a half-life of $1$ day. Another substance $B$ has an atomic mass number of $32$ and a half-life of $0.5$ day. If both $A$ and $B$ start undergoing radioactivity simultaneously with an initial mass of $320 \, g$ each,how many total atoms of $A$ and $B$ combined would be left after $2$ days? (Answer in $......... \times 10^{24}$)

The rate of disintegration of a radioactive sample is $R$ and the number of atoms present at any time $t$ is $N$. When $\frac{R}{N}$ is taken along the $Y$-axis and $t$ is taken along the $X$-axis,the correct graph is: