$1 \, mg$ of gold undergoes decay with a $2.7 \, \text{days}$ half-life period. The amount left after $8.1 \, \text{days}$ is ......... $mg$.

The activity of an element becomes $\frac{1}{64}$ of its original value in $60 \ s$. Then the half-life period is ............ $s$.

$N$ atoms of a radioactive element emit $n$ number of $\alpha$-particles per second. The mean life of the element in seconds is:

Two radioactive substances $A$ and $B$ have decay constants $5\lambda$ and $\lambda$ respectively. At $t = 0$,a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become $(1/e)^2$ will be

Radon-$222$ has a half-life of $3.8$ days. If one starts with $0.064 \ kg$ of radon-$222$, the quantity of radon-$222$ left after $19$ days will be (in $kg$)

The activity of a radioactive sample is $6000 \, dps$ after $280$ days. After another $140$ days,the activity decreases to $3000 \, dps$. The initial activity of the radioactive sample (in $dps$) is ........