The half life of a radioactive substance is $20$ minutes. In $........\,minutes$ time,the activity of substance drops to $\left(\frac{1}{16}\right)^{ th }$ of its initial value.

The half-life of $Au ^{198}$ is $2.7\, days.$ The activity of $1.50\, mg$ of $Au ^{198}$ if its atomic weight is $198\, g mol ^{-1}$ is .......$Ci$ $\left( N _{ A }=6 \times 10^{23}\, / mol \right)$

Radioactive material $'A'$ has decay constant $8 \lambda$ and material $'B'$ has decay constant $ ' \lambda '$. Initially they have same number of nuclei . After what time, the ratio of number of nuclei of material $'B'$ to that $'A'$ will be $\frac{1}{e}$ ?

The radioactivity of a certain radioactive elements drops to $\frac{1}{64}$ of its initial value in $30$ seconds. Its half life is ............. seconds

A radioactive material has a half life of $10$ days. What fraction of the material would remain after $30$ days

There are $10^{10}$ radioactive nuclei in a given radioactive element, Its half-life time is $1\, minute.$ How many nuclei will remain after $30\, seconds?$

$(\sqrt{2}=1.414)$