The half-life of a sample of a radioactive substance is $1 \text{ hour}$. If $8 \times 10^{10}$ atoms are present at $t = 0$,then the number of atoms decayed in the duration $t = 2 \text{ hours}$ to $t = 4 \text{ hours}$ will be

$A$ radioactive sample decays by two modes: $\alpha$-decay and $\beta$-decay. $66.6\%$ of the time it decays by $\alpha$-decay and $33.3\%$ of the time it decays by $\beta$-decay. If the effective half-life of the sample is $60 \text{ years}$,what will be the half-life of the sample if it decays only by $\alpha$-decay? (in years)

The half-lives of two radioactive materials $A$ and $B$ are $T$ and $2T$ respectively. If the ratio of the initial masses of the materials $A$ and $B$ is $8:1$, then the time after which the ratio of the masses of the materials $A$ and $B$ becomes $4:1$ is

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

The decay constant of a radioisotope is $\lambda$. If its activity at times $t_1$ and $t_2$ are $A_1$ and $A_2$ respectively,then the number of nuclei that have decayed during the time interval $(t_1 - t_2)$ is:

An active nucleus decays to one-third $\left(\frac{1}{3}\right)$ of its initial activity in $20 \text{ hours}$. The fraction of original activity remaining after $80 \text{ hours}$ is: