Two species of radioactive atoms are mixed in equal number. The disintegration constant of the first species is $\lambda$ and of the second is $\lambda / 3$. After a long time the mixture will behave as a species with mean life of approximately

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 $log_{10}e = 0.4343$ )

A radioactive substance has a half-life of $1$ year. The fraction of this material, that would remain after $5$ years will be

For a radioactive material, its activity $A$ and rate of change of its activity $R$ are defined as $A=-\frac{d N}{d t}$ and $R=-\frac{d A}{d t}$, where $N(t)$ is the number of nuclei at time $t$. Two radioactive sources $P$ (mean life $\tau$ ) and $Q$ (mean life $2 \tau$ ) have the same activity at $t=0$. Their rates of change of activities at $t=2 \tau$ are $R_p$ and $R_Q$, respectively. If $\frac{R_p}{R_Q}=\frac{n}{e}$, then the value of $n$ is

The half-life of $Au ^{198}$ is $2.7\, days.$ The activity of $1.50\, mg$ of $Au ^{198}$ if its atomic weight is $198\, g mol ^{-1}$ is .......$Ci$ $\left( N _{ A }=6 \times 10^{23}\, / mol \right)$

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