During the mean life of a radioactive element,the fraction that disintegrates is

$A$ radioactive material of half-life $2.5$ hours emits radiation that is $32$ times the safe maximum level. The time (in hours) after which the material can be handled safely is

The counting rate observed from a radioactive source at $t=0$ second was $1600$ counts per second and at $t=8$ seconds it was $100$ counts per second. The counting rate observed,as counts per second at $t=6$ seconds,will be

The decay constant for a radioactive nuclide is $1.5 \times 10^{-5} \, s^{-1}$. The molar mass of the substance is $60 \, g \, mol^{-1}$,$(N_A = 6 \times 10^{23})$. The activity of $1.0 \, \mu g$ of the substance is $....... \times 10^{10} \, Bq$.

$A$ radioactive sample of $U^{238}$ decays to $Pb$ through a process for which the half-life is $4.5 \times 10^9$ years. Find the ratio of the number of nuclei of $Pb$ to $U^{238}$ after a time of $1.5 \times 10^9$ years (given $2^{1/3} = 1.26$).

Two radioactive materials $A_1$ and $A_2$ have decay constants of $10 \lambda_0$ and $\lambda_0$. If initially they have the same number of nuclei,the ratio of the number of their undecayed nuclei will be $(1/e)$ after a time $t$. Find $t$.