The rate of disintegration was observed to be ${10^{17}}$ disintegrations per sec when its half life period is $1445$ years. The original number of particles are

A freshly prepared sample of a radioisotope of half-life $1386 \ s$ has activity $10^3$ disintegrations per second. Given that In $2=0.693$, the fraction of the initial number of nuclei (expressed in nearest integer percentage) that will decay in the first $80 \ s$ after preparation of the sample is :

For a substance the average life for $\alpha$-emission is $1620$ years and for $\beta$ emission is $405$ years. After how much time the $1/4$ of the material remains after $\alpha$ and $\beta$ emission …….$years$

The decay constants of a radioactive substance for $\alpha $ and $\beta $ emission are ${\lambda _\alpha }$ and ${\lambda _\beta }$ respectively. If the substance emits $\alpha $ and $\beta $ simultaneously, then the average half life of the material will be

A mixture consists of two radioactive material $A_1$ 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……….$sec$