Sec. 7.3] RADIOACTIVITY 165 



/. Alpha Decay. With a single exception (lithium) alpha-particle emission 

 is always monoenergetic. Although only one alpha particle is emitted per 

 disintegration, many energy groups may be observed corresponding to 

 different and more or less probable level transitions in the same species of 

 nucleus. The residual atom is smaller in charge by two electronic units and 

 is diminished in mass by an amount approximately equal to the rest mass of 

 the alpha particle plus the kinetic energies of the particle and recoil nucleus, 

 plus the rest mass of two electrons. 



7.2. Law of Radioactive Decay. Radioactive decay is a statistical process 

 following well-established rules. A single radioactive nucleus possesses a 

 fixed probability of disintegration per unit time which is characteristic of 

 the particular isotope and its state of excitation. Aside from these two 

 factors, the probability of decay, and hence the rate of decay of a macro- 

 scopic quantity of the radioisotope, is wholly independent of external 

 influences such as temperature, pressure, chemical reagents, and the means 

 by which it is produced. Since each disintegration is a statistically inde- 

 pendent event, the average number of nuclei which disintegrate per unit time 

 is proportional to the number of nuclei of the particular species in a pre- 

 scribed state of excitation that are present at any instant. 



f - - 



where N — number of nuclei present at time / 



X = disintegration constant; factor of proportionality characteristic 

 of the isotope and its state of excitation 

 In practice the quantity A r frequently is given any convenient dimension 

 and may be referred to as the number of nuclei, activity, mass, or some wholly 

 arbitrary unit convenient to the particular measuring device. 



7.3. Fluctuations. The actual number of disintegrations observed per unit 

 time fluctuates about a mean value A as a consequence of the random 

 character of the disintegration process. The probability of observing M 

 disintegrations per unit time when the average value is A is given by the 

 Poisson probability distribution formula: 



When the average value is large and the difference A — M is small, the 

 probability distribution may be represented approximately by Gauss' 

 formula; 



1 (M-XY- 



Pu = , e 7\— 



