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

$A$ wooden artifact and a freshly cut tree have carbon activity of $7.6$ and $15.2 \ min^{-1} g^{-1}$ respectively. Given the half-life $(t_{1/2})$ of carbon is $5760$ years,the age of the artifact is:

The half-life of $^{60}Co$ is $7 \ years$. If $1 \ g$ of it decays,the amount of the substance remaining after $28 \ years$ is (in $g$)

The half-life of $_{38}^{90}Sr$ is $20 \text{ years}$. If a sample having an initial activity of $8000 \text{ dis/min}$ is taken,what would be its activity after $80 \text{ years}$?

$A$ freshly prepared radioactive element has a half-life of $2 \ hr$. It emits radiation whose intensity is $64$ times the permissible safe level. The minimum time after which it would be possible to work with this sample is .......... $hr$.

$\frac{15}{16}$-th of a radioactive sample decays in $40$ days. The half-life of the sample is ...... days.