G78 Prof. E. Rutherford on the 



centre is given by 



it is not difficult to show that the deflexion (supposed small) 

 of an electrified particle due to this field is given by 



7 , o x 3 / 2 



-fc-b) - 



where p is the perpendicular from the centre on the path of 

 the particle and b has the same value as before. It is seen 

 that the value of 6 increases with diminution of p and becomes 

 great for small values of (/>. 



Since we have already seen that the deflexions become 

 very large for a particle passing near the centre of the atom, 

 it is obviously not correct to find the average value by 

 assuming 6 is small. 



Taking R of the order 10" 8 cm., the value oPjo for a large 

 deflexion is for a and fi particles of the order 10~ n cm. 

 Since the chance of an encounter involving a large deflexion 

 is small compared with the chance of small deflexions, a 

 simple consideration shows that the average small deflexion 

 is practically unaltered if the large deflexions are omitted. 

 This is equivalent to integrating over that part of the cross 

 section of the atom where the deflexions are small and 

 neglecting the small central area. It can in this way be 

 simply shown that the average small deflexion is given by 



. 3tt b 

 +i= 8"R- 



This value of xf> Y for the atom with a concentrated central 

 charge is three times the magnitude of the average deflexion 

 for the same value of N*? in the type of atom examined by 

 Sir J. J. Thomson. Combining the deflexions due to the 

 electric field and to the corpuscles, the average deflexion is 



«>i 2 + <£ 2 2 ) 2 or ^(5-54 + 



h ) 



It will be seen later that the value of 1ST is nearly proportional 

 to the atomic weight, and is about 100 for gold. The effect 

 due to scattering of the individual corpuscles expressed by 

 the second term of the equation is consequently small for 

 heavy atoms compared with that due to the distributed 

 electric field. 



