At time $t=0$ some radioactive gas is injected into a sealed vessel. At time $T$ some more of the gas is injected into the vessel. Which one of the following graphs best represents the logarithm of the activity $A$ of the gas with time $t$ ?

At $t = 0$, number of active nuclei in a sample is $N_0$. How much no. of nuclei will decay in time between its first mean life and second half life?

Activity of a radioactive sample decreases to $(1/3)^{rd}$ of its original value in $3\, days$. Then, in $9\, days$ its activity will become

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

The mean life time of a radionuclide, if its activity decrease by $4\%$ for every $1h$ , would be  ………. $h$ [product is non-radioactive i.e. stable]