The half-life of $10 \ g$ of a radioactive substance is $10 \ days$. The half-life of $20 \ g$ of the same substance is .......... $days$.

After $2 \, \text{hours}$,the amount of a certain radioactive substance reduces to $1/16^{th}$ of the original amount (the decay process follows first-order kinetics). The half-life of the radioactive substance is $...... \, \text{min}$.

The decay profiles of three radioactive species $A$,$B$ and $C$ are given below:
These profiles imply that the decay constants $k_A$,$k_B$ and $k_C$ follow the order:

$A$ radioactive isotope decays at such a rate that after $192 \ min$ only $1/16$ of the original amount remains. The half-life of the radioactive isotope is ....... $\min$

The unit of the decay constant for radioactive disintegration is:

If $1 \ \mu g$ of radium $(^{226}Ra)$ has disintegrated for $500$ years,how many alpha particles will be emitted per second?