If $3/4$ of a radioactive sample decays in $3/4 \, s$,then the half-life of the sample is ........ .

The half-life of radium is $1620$ years and its atomic weight is $226 \, g/mol$. What is the number of atoms decaying per second in a $1 \, g$ sample? $[N_A = 6.023 \times 10^{23} \, \text{atoms/mol}]$

Two different radioactive elements with half-lives $T_1$ and $T_2$ have undecayed atoms $N_1$ and $N_2$ respectively present at a given instant. The ratio of their activities at that instant is

$A$ radioactive substance has a half-life of $1$ year. The fraction of this material that would remain after $5$ years will be

$A$ mixture consists of two radioactive materials $A_1$ and $A_2$ with half-lives of $20 \ s$ and $10 \ s$ respectively. Initially,the mixture has $40 \ g$ of $A_1$ and $160 \ g$ of $A_2$. The amount of the two in the mixture will become equal after: (in $s$)

The half-life of a radioactive substance is $ 20 \text{ minutes} $. The time taken between $ 50\% $ decay and $ 87.5\% $ decay of the substance will be