FORCES AND ATOMS 353 



Are they short-range or long-range? By calling them "cohesive" I have 

 already committed myself, but correctly. There is an argument quite 

 similar to the second which I drew from the vaporization of liquids. Think 

 again of the kettle of water boiling away on the stove. It takes as much 

 energy from the flame to disperse the last cubic inch of water that goes as 

 it does to drive off the first, despite the fact that the first is exposed to all 

 the long-range forces of attraction exerted on it by all the other cubic inches 

 remaining in the kettle, and the last is not. Therefore the long-range 

 forces which act between atom and atom are trivial, and cohesion is a force 

 exerted by the atoms on their near neighbors only. Think now of the 

 cluster of protons and neutrons which is a nucleus — a massive one by choice, 

 built of two hundred particles or more. Imagine it taken to pieces by 

 detaching one particle after another. I admit that this precise experiment 

 is beyond the art of the physicist, but for a certain reason — the one which 

 I have already promised to give, and will give at the end — he is as confident 

 of its result, as he ever is of the result of any experiment which he has not 

 actually performed. The result is, that it takes roughly as much energy to 

 remove a particle when there are two hundred left behind to pull it back, 

 as when there are but a dozen left behind, or any number in between. 

 Therefore the long-range forces which act between the fundamental particles 

 are minor, and the intra-nuclear cohesion is a short-range force. 



I have carefully made these last statements rather weaker than their 

 analogues for the water boiling away. The amount of energy required for 

 taking away a particle does depend to some extent on the number left 

 behind, and the long-range forces are therefore minor but not trivial. If 

 the long-range forces are attractive, the binding-energy of a particle — this 

 is the shorter name which is given to the "energy required for taking away 

 a particle"^ — must be greater, the greater the size of the cluster, i.e., the 

 greater the mass of the nucleus. Now for nuclei of some fifty particles or 

 more, the contrary is the case. Therefore the long-range force, or the major 

 one if there are more than one, is a repulsion. We already know of one 

 long-range repulsion, to wit, the electrostatic force between proton and 

 proton. Is this the force in question? The answer is oddly difficult to 

 give with assurance, but at present is believed to be yes. 



If the answer is definitely yes, then the electrostatic force has after all one 

 role of supreme importance in nuclei. It fixes their maximum size and 

 their maximum charge, therefore limits the number of chemical elements, 

 and may indeed be all that prevents the universe from caving together into 

 a single lump of protons and neutrons with the electrons fluttering help- 



^It ought strictly to be called the "unbinding-energy" or "binding lack-of-energy," 

 since it is given as positive when energy must be contributed to the system in order to 

 detach the particle. 



