The half-life period of radioactive decay of ${}^{14}C$ is $5730 \ years$. An archaeological artifact contains $80\%$ of ${}^{14}C$ as compared to a living tree. Calculate the age of the sample in $years$.

The decay constant of a radioactive sample is $\lambda$. The half-life and mean life of the sample are respectively

$A$ wood specimen from an archeological site shows a $_6^{14}C$ activity of $5.0 \ counts/min/gm$ of carbon. If a freshly cut wood gives $15 \ counts/min/gm$ of carbon,what is the age of the specimen? (Given: $t_{1/2}$ for $_6^{14}C$ is $5000 \ years$)

$1.0 \ g$ of radioactive sodium decays to $0.25 \ g$ in $16 \ hours$. Calculate the time required for $48 \ g$ of the same radioactive sodium to decay to $3.0 \ g$. (in $hours$)

$A$ radioactive substance has a constant activity of $2000$ disintegrations/minute. The material is separated into two fractions,one of which has an initial activity of $1000$ disintegrations per minute while the other fraction decays with $t_{1/2} = 24 \ h$. The total activity in both samples after $48 \ h$ of separation is

The $T_{1/2}$ of $C^{14}$ isotope is $5770$ years. The time after which $72\%$ of the isotope is left is .......... years.