If $87.5\%$ of a given substance disintegrates in $40 \text{ minutes}$,what is the half-life of the radioactive substance?

The half-life of $_6C^{14}$ if its decay constant $k$ or $\lambda$ is $2.31 \times 10^{-4} \ yr^{-1}$ is:

$A$ 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:

The half-life period of a radioactive metal is $20 \ days$. What fraction of the metal remains after $80 \ days$?

$A$ radioactive element decays at such a rate that after $15 \ min$ only $1/10$ of the original amount is left. How many more minutes will be needed when only $1/100$ of the original amount will be left? .......... $\min$

For $Ra^{226}$,the $t_{1/2}$ is $1620 \ years$. From $0.001 \ g$ of $Ra$,how many $\alpha$-particles are released per $min$?