law of radioactivity:

Therefore, a convenient measure of how fast a radionuclide decays is in terms of half- life (t_½) of the radionuclide. A parameter half-life (t_½) is described as the time interval during which statistically large number of radioactive atoms undergoes decay and become half of the original number of atoms (N_o).  Therefore, according to Eq. (1), after one half-life there will be N_o/2 atoms. Therefore, half life and decay constant are related through

t_{1 / 2} = ln 2/λ = 0 .693/λ                                                     ............(1)

Since each radionuclide has its own characteristic decay constant, it has a definite half- life which varies in a larger range, as small as ∼ 10^-19 s for ⁹B to 10¹⁸ y for naturally occurring ²⁰⁹Bi. A mean life (τ) of a radionuclide is 1/ λ or 1.44 t_1/2.

Second law of radioactivity was proposed through Frederic Soddy and it is also known as group displacement law. As per that law, during α decay, parent decays to daughter where Z is decreased through two and it is displaced through two groups on the left in periodic table. Same, during β decay, Z is increased through one and the daughter nuclide is displaced through one position towards right in the periodic table.