652 TABLE 714.— PARTICLE ATTRACTION, VELOCITY, AND MASS 



The neutrons and protons are held together in a nucleus by attractive forces 

 (nuclear force) which have a range of only about 2 x 10~ 13 cm but are 

 stronger than the electric Coulomb forces at distances less than this range. 

 The energy which would be required to separate a nucleus into its constituent 

 protons and neutrons (collectively denoted by nucleons) is called the nuclear 

 binding energy. According to Einstein's mass-energy relation this binding 

 energy is equal to c 2 times the difference between the nuclear mass and the 

 mass in the free state of the nucleons contained in the nucleus. The binding 

 energy per nucleon is of the order of magnitude of a few Mev, its actual 

 amount depending on various factors. Starting at about 1 Mev for the deu- 

 teron (nucleus of heavy hydrogen) the binding energy per nucleon increases 

 on the average with increasing atomic weight A reaching a maximum of about 

 10 Mev for A about 50 ; as A increases further the Coulomb repulsion between 

 the constituent protons becomes more and more important and the binding 

 energy per particle decreases again. In addition to this general trend there are 

 individual variations in stability, a notable example being the great stability 

 of the a-particle (nucleus of He 4 ) with a binding energy of more than 7 Mev 

 per nucleon. 



The theory of relativity shows that energy and mass are related and that 

 mass may be converted into energy, giving an amount of energy in ergs = mc 2 , 

 where c is the velocity of light expressed in cm/sec and m the mass in grams. 

 This theory also shows that the velocity of light is the upper limit for the 

 velocity for any particle. It is to be noted that this theory tells us nothing as 

 to the method of converting mass to energy ! 



The mass m of a fast-moving particle depends upon its velocity v, thus, m 

 / yyt 

 (at velocity v) = where ft = v/c. The kinetic energy of a particle 



V *■ p 



moving with a velocity near that of light 



"-"■KvT^- 1 ) 



or 



m = m + 



KE 



Some calculated results of the above relations are shown in Table 713. This 

 theory, together with nuclear physics, shows that each moving particle has a 

 wavelength that is given thus: the wavelength, A = h/mv for a particle of 

 mass m with a velocity v. (See Table 722.) 



TABLE 715.— TWO INTERESTING RESULTS OF ARTIFICIAL 

 DISINTEGRATION* 



Different results 

 from the same material 



»AF + iHe 4 -»,.?" + tit 1 

 uAP + iHe'-^Si 30 + .H 1 

 uAF + jrT-^Mg 26 + ,He 4 

 13 AP + 1 H 2 _^ 13 Ar M -|- 1 H 2 

 i.AP -(- .H 1 _> ^Si 27 + on 1 

 i.Al w + on 1 _> uAl 28 + hv 

 uAl" + on 1 _> M Mfr w + ^H 1 

 uAl 27 + „H 1 -^ 11 Na 24 - r - ? He 4 



Different ways of 

 producing the same materials 

 12 Mg 25 + ,He 1 --M,Al 28 + >H 1 

 uAl" + iH , _*,Al* + .H 1 

 aAI" + on'-nsAl 28 + hv 

 14 Si 28 + oH l _ M ,Al 28 4-.H 1 

 i.P n + .» 1 ->i3Al" + .He 4 



For reference, see footnote 224, 



665. 



SMITHSONIAN PHYSICAL TABLES 



