The half-life of a radioisotope is $20 \ hours$. After $60 \ hours$,what fraction of the initial amount will remain?

If $n_t$ number of radioatoms are present at time $t$,the following expression will be a constant:

$^{226}Ra$ disintegrates at such a rate that after $3160 \ years$ only one-fourth of its original amount remains. The half-life of $^{226}Ra$ will be .......... $years$.

The half-life for radioactive decay of $^{14}C$ is $5730 \text{ years}$. An archaeological artifact containing wood had only $80\%$ of the $^{14}C$ found in a living tree. Which is the correct formula for age $(t)$ of the sample?

In the case of a radioisotope,the value of $T_{1/2}$ and $\lambda$ are identical in magnitude. The value is

$A$ piece of wood from an archaeological sample has $5.0 \text{ counts min}^{-1} \text{ g}^{-1}$ of $^{14}C$,while a fresh sample of wood has a count of $15.0 \text{ counts min}^{-1} \text{ g}^{-1}$. If the half-life of $^{14}C$ is $5770 \text{ yr}$,the age of the archaeological sample is: