$A$ radioactive sample $(Z = 22)$ decreases by $90\%$ in $10 \ \text{years}$. What will be the half-life of the sample in $\text{years}$?

The half-life of the radioactive isotope tritium $(_1^3H)$ is $12.3 \ years$. If the initial amount of tritium is $32 \ mg$,how many milligrams will remain after $49.2 \ years$ (in $mg$)?

$A$ radioactive substance has a half-life $(t_{1/2})$ of $60 \ minutes$. After $3 \ hours$,what percentage of the radioactive substance will remain?

Assuming $1 \, \mu g$ of trace radioactive element $X$ with a half-life of $30 \ years$ is absorbed by a growing tree. The amount of $X$ remaining in the tree after $100 \ years$ is $n \times 10^{-1} \, \mu g$. Find the value of $n$. $[Given : \ln 10 = 2.303 ; \log 2 = 0.30]$

$1.0 \ g$ of radioactive sodium decays to $0.25 \ g$ in $16 \ hours$. Calculate the time required for $48 \ g$ of the same radioactive sodium to decay to $3.0 \ g$. (in $hours$)

$^{18}_{8}O$ has a half-life of $4650 \text{ years}$. $200 \text{ mg}$ of a sample of $^{18}_{8}O$ is reduced to $25 \text{ mg}$ in ......... $\text{years}$.