CONTEMPORARY ADVANCES IN PHYSICS 633 



air, and depends in a known way (known by experiment) on the speed 

 which the particle had at the moment of entry. Or the range may be 

 determined by moving backward a fluorescent screen placed opposite 

 the point of entry of the corpuscles; the scintillations are at first undim- 

 inished in number as the screen recedes, but eventually they cease, and 

 cease quite suddenly; the distance to the point of their cessation is the 

 range. In air at normal pressure and 15° temperature,^ the range of 

 the fastest known alpha-particles (apart from a few very scanty classes) 

 fresh from the source is about 8.6 cm. It has been determined for a 

 number of other gases as well, and for any gas it varies inversely as the 

 density. 



It follows then that if the fluorescent screen is placed at a distance 

 from the source of alpha-particles so great that it lies beyond their 

 range in the substance intervening, whatever scintillations may appear 

 upon it are not due to alpha-rays. But it does not yet follow that the 

 screen is beyond the reach of protons speeded up in the way I just de- 

 scribed. To find out about this, it is necessary to know the relation 

 between the speeds of protons and their ranges. Now the cause of the 

 slowing-down and stopping of charged corpuscles, protons and alpha- 

 particles alike, is this: as they flash through strata of matter, they tear 

 electrons loose from the atoms which they pass, and spend their 

 energy in doing so. The range of either sort of corpuscle is substan- 

 tially the distance through which it can fly, before the major part of its 

 initial energy is dissipated in this way. An alpha-particle has twice 

 the charge of a proton, therefore extracts electrons oftener from the 

 atoms near its course, therefore loses energy more quickly. If particles 

 of the two kinds have equal range, the former must initially have had 

 the greater energy. A theoretical analysis (achieved by Bohr and 

 Darwin) shows that the ratio is that of the squares of the charges- 

 four to one. But since the ratio of the masses is likewise four to one, 

 the speeds are equal. Alpha-particles and protons of equal initial 

 speed have (approximately) equal range. Now as I stated above, 

 hydrogen nuclei struck centrally by alpha-particles acquire a speed 1.6 

 times as great as these, therefore, a range equal to that of alpha-parti- 

 cles moving 1.6 times as fast as those which made the impacts. It is a 

 fact of experience that the range of alpha-particles varies about (not 

 exactly) as the cube of their speed. If, therefore, hydrogen is bom- 

 barded by rays of a stated range R, hydrogen nuclei which suffer 

 central impacts will be projected forward with ranges amounting to 

 1 This is Rutherford's convention. Certain physicists specify the range in air at 

 normal pressure anci zero temperature, which stands to the other in the mverse ratio 

 of the densities of the air, about 273 : 288. In later pages I shall occasionally adopt 

 this usage. 



