The activity of a radioactive sample reduces from $A_0$ to $\frac{A_0}{\sqrt{3}}$ in $1$ hour. What will be the activity after $3$ hours more?

The activity of a radioactive sample is $6000 \, dps$ after $280$ days. After another $140$ days,the activity decreases to $3000 \, dps$. The initial activity of the radioactive sample (in $dps$) is ........

If the radioactive decay constant of radium is $1.07 \times 10^{-4}$ per year,then its half-life period is approximately equal to ......... $years$.

$A$ radioactive substance has decay constants $\lambda_{\alpha}$ and $\lambda_{\beta}$ for $\alpha$ and $\beta$ emission,respectively. If the substance emits both $\alpha$ and $\beta$ particles,find the effective half-life of the substance.

Give the different units of radioactivity and define them.

The half-life of a radioactive substance is $10 \, \text{minutes}$. If $n_1$ and $n_2$ are the number of atoms decayed in $20 \, \text{minutes}$ and $30 \, \text{minutes}$ respectively, then $n_1 : n_2 =$