In the radioactive decay of an element,it is found that the count rate reduces from $1024$ to $128$ in $3$ minutes. Its half-life will be ...... minutes.

Half-lives of two radioactive nuclei $A$ and $B$ are $10 \, minutes$ and $20 \, minutes$,respectively. If,initially,a sample has an equal number of nuclei,then after $60 \, minutes$,the ratio of the number of decayed nuclei of $A$ and $B$ will be:

$A$ radioactive element has a rate of disintegration $10,000$ disintegrations per minute at a particular instant. After four minutes it becomes $2500$ disintegrations per minute. The decay constant per minute is (in $log _e 2$)

The activity of a freshly prepared radioactive sample is $10^{10}$ disintegrations per second,whose mean life is $10^9 \ s$. The mass of an atom of this radioisotope is $10^{-25} \ kg$. The mass (in $mg$) of the radioactive sample is

The half-life of a substance is $20 \ min$. The time taken between $33\%$ decay and $67\%$ decay will be ....... $min$.

Define the decay constant and state its $SI$ unit.