$8 \, g$ of the radioactive isotope,cesium$-137$ were collected on February $1$ and kept in a sealed tube. On July $1$,it was found that only $0.25 \, g$ of it remained. So the half-life period of the isotope is ....... $days$.

The half-life period of a radioactive element is $140$ days. After $560$ days,one gram of the element will reduce to

${ }^{227}Ac$ has a half-life of $22 \, years$ with respect to radioactive decay. The decay follows two parallel paths: ${ }^{227}Ac \longrightarrow { }^{227}Th$ and ${ }^{227}Ac \longrightarrow { }^{223}Fr$. If the percentage of the two daughter nuclides are $2.0$ and $98.0$,respectively,the decay constant (in $year^{-1}$) for ${ }^{227}Ac \longrightarrow { }^{227}Th$ path is closest to

The disintegration constant for a radioactive substance is $0.58 \, hr^{-1}$. Its half-life period is $........ \, hr$.

$A$ radioactive isotope having a half-life of $3 \ days$ was received after $12 \ days$. It was found that there were $3 \ g$ of the isotope in the container. The initial weight of the isotope when packed was ......... $g$.

$A$ radioactive element has a half-life of $20 \ \text{minutes}$. How much time should elapse before the element is reduced to $\frac{1}{8}$th of the original mass? (Answer in $\text{minutes}$)