If a substance with a half-life of $3 \ days$ is kept for $12 \ days$,what fraction of the substance remains?

Radium has an atomic weight of $226$ and a half-life of $1600$ years. The number of disintegrations produced per second from $1 \ g$ of radium is:

${ }^{227}Ac$ 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

After $2 \, \text{hours}$,the amount of a certain radioactive substance reduces to $1/16^{th}$ of the original amount (the decay process follows first-order kinetics). The half-life of the radioactive substance is $...... \, \text{min}$.

The half-life of a radioactive isotope is $4 \ hours$. If the initial mass of the isotope is $200 \ g$,then what will be the disintegrated amount of it after $16 \ hours$?

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 $years$.