604 ADOLF F. VOIGT 



The atomic number is thereby reduced by one in contrast to the nega- 

 tive j8-ray process, in which the atomic number increases by one. In 

 positron emission the nucleus gives off a positron, which has an energy 

 distribution Uke that of the electron. A positron does not have a 

 long life; as soon as it is slowed down by collisions to nearly zero 

 kinetic energy, it interacts with an electron in some atom to annihilate 

 the pair and produce two 7 rays, each of which has an energy equiva- 

 lent to the mass of the electron at rest (0.51 m.e.v.). If a nucleus is 

 unstable to this type of transition (if it must reduce its charge in its 

 decay process) but does not have enough energy to create a positron, 

 it may capture one of the innermost (K) electrons around it. This 

 process is accompanied by X rays given off when the K shell is re- 

 filled, and usually by 7 radiation. 



An additional type of decaj'^ is found in some of the cases of nu- 

 clear isomerism (the existence of nuclear species with the same atomic 

 number and mass but different nuclear properties), in which transi- 

 tion between isomers occurs. Since no charged particle can be emit- 

 ted from the nucleus mthout changing Z, such decay is characterized 

 only by 7-ray emission (but, in addition, electrons may be expelled 

 from the atom owing to the internal conversion of these 7 rays, and 

 then X rays would accompany the conversion process) . 



2. Radioactive Decay Law 



Radioactive decay is governed by the familiar first order rate equa- 

 tion: 



~dN/dt = XN 



in which —dN/dt is the number of disintegrations per unit time, X is 

 the decay constant, or decay probability, and N is the number of 

 radioactive atoms present. Integrated forms of this equation are : 



N = Noe-"-' and logio (No/N) = (X//2.303) 



in which No is the number of atoms at time t = 0. From this law it 

 follows that the fraction decaying in time dt is X and is thus indepentl- 

 ent of the amount present. The rate of decay is usually stated in 

 terms of the time required for one-half to decay; this time is called 

 the half-life and is related to the decay constant l\y the equation: 



iu^ = 0.693/X 



