If the half-life of a substance is $5 \, \text{years}$,then the total amount of substance left after $15 \, \text{years}$,when the initial amount is $64 \, \text{grams}$,is ....... $\text{gm}$.

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

$t_{1/2}$ of $^{232}Th$ is $1.39 \times 10^{10} \ \text{years}$. Calculate the number of $\alpha$-particles emitted by $1.0 \ \text{g}$ of $^{232}Th$ per second.

$10 \ g$ of a radioactive element is disintegrated to $1 \ g$ in $2.303 \ \text{minutes}$. What is the half-life (in minutes) of that radioactive element?

${ }^{227}Ac$ 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

$A$ radioactive element has a half-life of $1 \text{ day}$. After $3 \text{ days}$,the amount of the element left will be: