An archaeologist analyses the wood in a prehistoric structure and finds that ${C^{14}}$ (Half life $= 5700\, years$) to ${C^{12}} $ is only one- fourth of that found in the cells buried plants. The age of the wood is about ........$years$

The half-life of a radioactive substance is $40$ years. How long will it take to reduce to one fourth of its original amount and what is the value of decay constant

The half life of a radioactive substance is $20$ minutes. In $........\,minutes$ time,the activity of substance drops to $\left(\frac{1}{16}\right)^{ th }$ of its initial value.

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 period of radioactive element ${x}$ is same as the mean life time of another radioactive element $y.$ Initially they have the same number of atoms. Then:

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 ...... minute