The half-life of radioactive Radon is $3.8 \ days$. The time at the end of which $1/20^{th}$ of the Radon sample will remain undecayed is ........... $days$ (Given $\log_{10} e = 0.4343$).

Half-life of a radioactive substance $A$ is two times the half-life of another radioactive substance $B$. Initially, the number of nuclei of $A$ and $B$ are $N_A$ and $N_B$ respectively. After three half-lives of $A$, the number of nuclei of both are equal. Then $\frac{N_A}{N_B}$ is

$A$ radioactive substance of half-life $138.6 \text{ days}$ is placed in a box. After $n$ days, only $20\%$ of the substance is present. Then the value of $n$ is $[\ln(5) = 1.61]$.

At time $t=0$,a container has $N_{0}$ radioactive atoms with a decay constant $\lambda$. In addition,$c$ number of atoms of the same type are being added to the container per unit time. How many atoms of this type are there at $t=T$?

In a sample of radioactive material,what fraction of the initial number of active nuclei will remain undisintegrated after half of a half-life of the sample?

Two radioactive isotopes $P$ and $Q$ have half-lives $10 \text{ minutes}$ and $15 \text{ minutes}$ respectively. Freshly prepared samples of each isotope initially contain the same number of atoms. After $30 \text{ minutes}$,the ratio $\frac{\text{number of atoms of } P}{\text{number of atoms of } Q}$ will be