3o8 



Stippleiiient to "'^ Nature^' August 25, 1923 



distance of travel of the «-particle before it comes to 

 rest. It is clear from this, for a given velocity of o- 

 particle, that there must be a momentary equilibrium 

 between the number of He^. and 116,.+ particles such 

 that, on the average, the numl)er of captures in a given 

 small distance is equal to the number of losses. 



It is very convenient to suppose that for a given 

 velocity each He+ ^ particle has a mean free path Aj 

 cm. in the material before it captures an electron, and 

 the He+ particle a mean free path Aj cm. before it 

 loses its attendant electron. No doubt some of the 

 individual particles travel distances much shorter or 

 longer than this mean distance before either capture or 

 loss, but in considering a large number of particles we 

 may suppose there is an average distance traversed 

 l:)efore capture or loss, to be called the mean free path. 



When Nj He^.^. particles traverse a small distance 

 dx of a material the number which capture electrons is 

 Ni(/.v/Ai. If Ng He 4. particles are present the number 

 which lose an electron is ^^xjX^. But we have seen 

 that when an equilibrium is set up, the number of cap- 

 tures in a given distance must equal the number of 

 losses. Equating these two expressions, it is seen that 

 N2/N1 = Aj/Aj, or, in other words, the relative number of 

 He+ to He4.+ particles is proportional to the ratio of 

 the mean free path for loss to that for capture. Since 

 by the scintillation method the ratio Ng/Nj can be 

 measured for any velocity, by using different thick- 

 nesses of absorber we can thus determine the ratio of 

 the mean free paths for capture and loss for any 

 velocity. 



The actual value of the mean free path Aj of the 

 He,,, particle before it loses its electron can be directly 

 determined by experiment. Suppose the microscope is 

 focussed on the midway band of Fig. 2 and the number 

 of scintillations per minute observed in a good vacuum. 

 If the pumps are shut off and a small quantity of air or 

 other gas is introduced into the apparatus, the number 

 of scintillations is found to diminish with increasing 

 pressure of the air until the band has completely dis- 

 appeared. This takes place at quite a low pressure of 

 air, for example, for a pressure of about 1/4 mm. in the 

 box. 



The explanation of this result is obvious. The IIe+ 

 particles which escape from the mica occasionally 

 collide with an atom of the gas in its path, and the 

 electron which it captured in passing through the mica 

 is removed. In such a case the He+ becomes again an 

 He^.+ particle, and the latter is twice as easily de- 

 flected in a magnetic field as the former. Suppose the 

 collision occurs lor the first time at the point P (Fig. i). 

 The particle after losing its electron travels along a 

 new path shown in the figure, and the particle no 

 longer strikes the part of the screen viewed by the 



microscope. It is found that the numljcr of .scintill;i 

 tions seen in the micro.scopc falls off a< < ur<liii:; to ai 

 exponential law as the pressure of th< usid. 



.Such a result is to be expected, and from ilui data t he- 

 average distance which the He+ i>article traversts 

 before it loses its electron can be simply deduced. 

 Certain small corrections are necessary to take int. 

 account the finite width of the band of scintillations a 

 seen in the microscope, but we need not enter int 

 details at this stage. It is convenient to express tl 

 mean free path Aj in air of the He+ particles, not as tl 

 average length of path traversed in the rarefied g.i 

 before loss, but as the distance traversed in the sam 

 gas at standard pressure and temperature. For ex 

 ample, in a certain experiment, the mean free path in 

 air of the particle was found to be 12 cm. at a pressur< 

 of 0-040 mm. ; this corresponds to a mean free path 1 

 0-0063 mm. at standard pressure and temperature. 



In this way the mean free path in air Ijefore loss ••( 

 an electron has been measured for different velocitic 

 and it has been found over a considerable range th;i 

 the mean free path varies directly as the velocity of tli' 

 a-particle, so that the mean free path becomes shorter 

 as the velocity of the a-particle diminishes. Since w. 

 may regard the loss of an electron from the singl 

 charged particle as the result of a process of ionisation, 

 such a relation is to be expected, and indeed, if we tak- 

 into account the strong binding of a single electron li. 

 the He^^. nucleus, the mean free path for loss is of 

 the same order as that calculated from consideration 

 of the number of ions per cm. produced by the " 

 particle in air and other gases. Comparisons ha\ > 

 been made of the mean free path in air with that in 

 hydrogen and helium. Its value is 4 to 5 times longer 

 in hydrogen and more than 5 times longer in helium. 



Now that the mean free path Aj is known, the value 

 of Aj for capture can be deduced if the ratio Nj/Nj 1 

 also known. A difficulty, however, arises at this point. 

 In order to measure the ratio N^Nj it is necessary that 

 the active source should be covered with mica or other 

 solid material. Gas cannot be used conveniently. It 

 was found, however, that the ratio N2/N1 was the same 

 within the limits of error whether the o-particles were 

 reduced in velocity by passage through celluloid, mica, 

 aluminium, or silver. For this purpose the mica was 

 kept the same and a very thin sheet of the substance 

 under examination spread over it. The thickness of 

 the sheet was sufficient to set up a new equilibrium 

 between the singly and doubly charged particles, but 

 not sufficient to alter materially the velocity of the 

 ionising rays. 



Since the value of the ratio N^/N^ suffers no appreci- 

 able change for absorbers of such different atomic 

 weights, we may safely conclude that the ratio for a 



i 



