$A$ radioactive isotope has a half-life of $10 \ days$. If today $125 \ mg$ is left over,what was its original weight $40 \ days$ earlier?

Half-life is the time in which $50\%$ of a radioactive element disintegrates. Carbon-$14$ disintegrates $50\%$ in $5770$ years. Find the half-life of carbon-$14$ in 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

What is the half-life (in $\text{min}$) of a radioactive substance if $75\%$ of a given amount of the substance disintegrates in $30 \, \text{min}$?

What is the value of the decay constant of a compound having a half-life time $T_{1/2} = 2.95 \text{ days}$?

$A$ sample of rock from the moon contains an equal number of atoms of uranium and lead ($t_{1/2}$ for $U = 4.5 \times 10^9$ years). The age of the rock would be: