$A$ radioactive material whose half-life period is $2$ years weighs $1 \,g$ and is stored in the laboratory for $4$ years. Then the amount of remaining radioactive material is (in $\,g$)

The mean life of a radioactive material for alpha decay and beta decay are,respectively,$1620$ years and $520$ years. What is the half life of the sample (in years)?

Write down the definition and formula of half-life of a radioactive substance.

The relation between $\lambda$ and $T_{1/2}$ is ($T_{1/2} = \text{half-life}$,$\lambda = \text{decay constant}$)

The half-life period of a radioactive sample is $3.8 \ days$. After how many days will the sample become $\frac{1}{8}$ of the original substance?

An ancient discovery found a sample where $75 \%$ of the original carbon $(C^{14})$ remains. The age of the sample is: $\left(T_{1/2}(C^{14}) = 5730 \text{ years}, \ln 0.5 = -0.7, \ln 0.75 = -0.3\right)$ (in $\text{ years}$)