In the radioactive decay of an element,it is found that the count rate reduces from $1024$ to $128$ in $3$ minutes. Its half-life will be ...... minutes.

$A$ parent nucleus $X$ undergoes $\alpha$-decay with a half-life of $75000 \text{ yrs}$. The daughter nucleus $Y$ undergoes $\beta$-decay with a half-life of $9 \text{ months}$. In a particular sample,it is found that the rate of emission of $\beta$-particles is nearly constant (over several months) at $10^{7} / \text{h}$. What will be the number of $\alpha$-particles emitted in an hour?

$A$ certain radioactive substance has a half-life of $5\, years$. Thus, for a nucleus in a sample of the element, the probability of decay in $10\, years$ is ......... $\%$

The natural logarithm of the activity $R$ of a radioactive sample varies with time $t$ as shown. At $t=0$,there are $N_0$ undecayed nuclei. Then,$N_0$ is equal to [Take $e^2=7.5$].

Activity of a radioactive sample is $R_1$ at a time $t_1$ and $R_2$ at a time $t_2$. Its half-life period is $T$. The number of atoms that have disintegrated in the time interval $(t_2 - t_1)$ is equal to $\frac{n(R_1 - R_2)T}{\ln 4}$. Then '$n$' is equal to

Radon-$222$ has a half-life of $3.8$ days. If one starts with $0.064 \ kg$ of radon-$222$,the quantity of radon-$222$ left after $19$ days will be (in $kg$)