The half-life of $Bi^{210}$ is $5 \ days$. What time is taken by $(7/8)^{th}$ part of the sample to decay?

$A$ piece of wood from a recently cut tree shows $20$ decays per minute. $A$ wooden piece of the same size placed in a museum (obtained from a tree cut many years back) shows $2$ decays per minute. If the half-life of $C^{14}$ is $5730$ years,then the age of the wooden piece placed in the museum is approximately ........... years.

$A$ radioactive element initially has $4 \times 10^{16}$ active nuclei. If its half-life is $10 \ days$,find the number of nuclei that have decayed in $30 \ days$.

The half-life of a radioactive element $X$ is equal to the mean life of another radioactive element $Y$. Initially, the number of atoms for both is the same. Then:

What is the mass of $1 \, \text{curie}$ of $U^{234}$?

If there is $0.1 \ mg$ of radioactive $Th^{234}$, how much of it will remain undecayed after $120 \ \text{days}$, given its half-life is $24 \ \text{days}$? (Answer in $\mu g$)