The half-life of $^{215}At$ is $100 \,\mu s$. After how much time (in $\mu s$) will $1/16^{th}$ of the sample remain undecayed?

In the figure,$X$ represents time and $Y$ represents the activity of a radioactive sample. The activity of the sample varies with time according to which curve?

$A$ fraction $f_1$ of a radioactive sample decays in one mean life,and a fraction $f_2$ decays in one half-life.

$A$ radioactive material is reduced to $1/8$ of its original amount in $3$ days. If $8 \times 10^{-3} \, kg$ of the material is left after $5$ days,the initial amount of the material is $....... \, g$.

$A$ sample initially contains $10^{20}$ radioactive atoms. The number of $\alpha$-particles emitted in the third year is $0.3$ times the number of $\alpha$-particles emitted in the second year. How many $\alpha$-particles are emitted in the first year?

$A$ radioactive sample decays at a rate of $5000$ disintegrations/minute at a certain instant. After $5$ minutes, the rate becomes $1250$ disintegrations/minute. The decay constant is ....... (in $\ln 2$)