$Rn$ decays into $Po$ by emitting an $\alpha$-particle with a half-life of $4 \text{ days}$. $A$ sample contains $6.4 \times 10^{10}$ atoms of $Rn$. After $12 \text{ days}$,the number of atoms of $Rn$ left in the sample will be:

In a radioactive material,the activity at time $t_{1}$ is $R_{1}$ and at a later time $t_{2}$,it is $R_{2}$. If the decay constant of the material is $\lambda$,then:

The half-life of a radioactive element which has only $\frac{1}{32}$ of its original mass left after a lapse of $60\, days$ is ........ $days$.

Consider a radioactive nuclide which follows the decay rate given by $A(t) = A_0 2^{-(t/t_0)}$, where $A(t)$ is the fraction of radioactive material remaining after time $t$ from the initial $A_0$ at zero time. Let $A_1$ be the fraction of original activity which remains after $120 \ h$. Likewise, $A_2$ is the fraction of original activity remaining after $200 \ h$. If $A_1/A_2 = 16$, then the half-life $(t_0)$ will be: (in $h$)

$A$ 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 $\ln 2$)

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