A radioactive material of half-life $T$ was produced in a nuclear reactor at different instants, the quantity produced second time was twice of that produced first time. If now their present activities are $A_1$ and $A_2$ respectively then their age difference equals :
$\frac{T}{{\ln \,2}}\,\left| {\ln \,\frac{{{A_1}}}{{{A_2}}}} \right|$
$T\,\left| {\ln \,\frac{{{A_1}}}{{{A_2}}}} \right|$
$\frac{T}{{\ln \,2}}\,\,\left| {\ln \,\frac{{{A_2}}}{{2{A_1}}}} \right|$
$T\,\left| {\ln \,\frac{{{A_2}}}{{2{A_1}}}} \right|$
In the uranium radioactive series, the initial nucleus is $_{92}{U^{238}}$ and the final nucleus is $_{82}P{b^{206}}$. When the uranium nucleus decays to lead, the number of $\alpha - $ particles emitted 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 sample of a radioactive substance has $10^6$ nuclei. Its half life is $20 \,s$. The number of nuclei that will be left after $10 \,s$ is nearly ...... $\times 10^5$
The nuclide $^{131}I$ is radioactive, with a half-life of $8.04$ days. At noon on January $1$, the activity of a certain sample is $60089$. The activity at noon on January $24$ will be
A piece of wood from a recently cut tree shows $20\,decays$ per minute. A wooden piece of same size placed in a museum ( obtained from a tree cut many years back) shows $2\,decays$ per minute. If half life of $C^{14}$ is $5730\, years$, then age of the wooden piece placed in the museum is approximately ........... $years$