The initial activity of a radioactive element is $1600$. After $t = 8 \, s$,the activity becomes $100$. What is the activity at $t = 6 \, s$?

The half-life of a radioactive nuclide is $40 \, \text{hours}$. Find the fraction of the substance that has decayed after $20 \, \text{hours}$.

$A$ radioactive substance contains $10000$ nuclei and its half-life period is $20$ days. The number of nuclei present at the end of $10$ days is

The half-life of the radioisotope tritium $(_1^3H)$ is $12.3$ years. If the initial amount of tritium is $32 \ mg$, how much amount (in $mg$) will remain after $49.2$ years?

Starting with a sample of pure ${}^{66}Cu$, $7/8$ of it decays into $Zn$ in $15 \ minutes$. The corresponding half-life is ................ $minutes$.

Two radioactive materials $X_1$ and $X_2$ contain the same number of nuclei. If $6\lambda \, s^{-1}$ and $4\lambda \, s^{-1}$ are the decay constants of $X_1$ and $X_2$ respectively,the ratio of the number of undecayed nuclei of $X_1$ to that of $X_2$ will be $\left( \frac{1}{e} \right)$ after a time: