Laws of Radioactivity

All radionuclides do not decay at the same rate.  From the kinetics point of view disintegration of any radionuclide is a first order process. There are two laws of radioactivity. As according to the first law of the radioactivity, the rate of disintegration of a radionuclide at any time is directly proportional to the number of atoms present at that time.  Therefore,

- dN / λN = dt                                       .........................(1)

where, N is the number of radioactive atoms of a specific radionuclide present at time t and λ is the nuclear decay constant (in s^-1), a characteristic property of the radionuclide. The minus sign in Eq. (1) indicates that decay results in a decrease in number of atoms.  The probability in which a radionuclide will disintegrate in a certain time interval does not depend on the state of chemical combination, the temperature, pressure or the presence of other atoms.  At integrating Eq. (2), we get

N = N _ºe ^-λt                         ................ (2)

where, N_o is the number of radioactive atoms present in the starting (at t = 0). It means that during the time interval t, (N_o - N) radioactive atoms would have undergone radioactive decay.  Because Eq. (12.2) is exponential in nature and a plot of N vs. t (as shown in Figure) displays that radioactive decay never ceases or the number of radioactive atoms never becomes zero.

Figure: Decay plot of radioactive elements with time