What is the half-life of a radioactive substance if $87.5\%$ of any given amount of the substance disintegrates in $40 \, min$?

The amount of $_{53}I^{128}$ $(t_{1/2} = 25 \ min)$ remaining after $75 \ min$ is:

$A$ radioactive isotope has a half-life of $20 \ days$. If $100 \ g$ of the substance is taken,the weight of the isotope remaining after $40 \ days$ is ......... $g$.

${ }^{227}Ac$ 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

If the half-life of a certain radioactive nucleus is $1000 \ s,$ the disintegration constant is

$A$ radioactive element gets spilled over the floor of a room. Its half-life period is $30$ days. If the initial activity is ten times the permissible value,after how many days will it be safe to enter the room?