If the half-life of an isotope $X$ is $10 \ yr$,its decay constant is (in $yr^{-1}$)

The activity of carbon-$14$ in a piece of an ancient wood is only $12.5\%$. If the half-life period of carbon-$14$ is $5760 \, years$,the age of the piece of wood will be $(\log \, 2 = 0.3010)$

If the amount of radioactive substance is increased three times,the number of atoms disintegrated per unit time would

The half-lives of two radioactive nuclides $A$ and $B$ are $1 \ min$ and $2 \ min$ respectively. Equal weights of $A$ and $B$ are taken separately and allowed to disintegrate for $4 \ min$. What will be the ratio of weights of $A$ and $B$ disintegrated?

$^{18}_{8}O$ has a half-life of $4650 \text{ years}$. $200 \text{ mg}$ of a sample of $^{18}_{8}O$ is reduced to $25 \text{ mg}$ in ......... $\text{years}$.

${ }^{227}Ac$ 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