﻿the Electron Theory of Solids. 



671 



in this expression the only factor which varies from one metal 



to another is fp, the number of electrons made up into 



chains ; the conductivities of metals at the same tempera! ure 



are directly proportional to the number of electrons in unit 



volume which take part in carrying the current. 



We can put the expression for the conductivity in the 



form 



- e 2 c 

 gfp . 



If we take gcjv at 15° C. to be 10~ 13 , since 



£ 2 /m = 2'8xl0- 13 , 



the conductivity at this temperature is equal to 



fp x 2-8 Xl0" 26 . 



The values of / calculated from this expression for some 

 metals are given in Table I. 



Metal. 



Lithium ... 

 Sodium ... 

 Potassium 

 Rubidium 

 •Caesium ... 

 Calcium ... 

 Magnesiu m 



Zinc 



Cadmium... 

 Aluminium 



Table I. 







Conductivity 





/• 



at 15°. 



p. 



1-lXlO -4 



•25X10 23 



•16 



20 ., 



•15 „ 



•47 



1'4 „ 



•07 „ 



•70 



•83 „ 



'06 „ 



•50 



•5 ,, 



•048 „ 



•35 



1'3 „ 



•25 „ 



•19 



2-3 „ 



•48 „ 



•17 



1-65 ., 



•75 „ 



•08 



1'3 „ 



•50 „ 



•09 



3-3 „ 



1-0 „ 



•12 



i r . nnfcnssinm 



has a irmr.h 



\i) I'O'Pl' 



rentage of its electrons moving about in chains than any 

 other metal. 



To form an estimate of the average number of electrons 

 in a chain and the velocities of the chains, we may proceed 

 as follows : — If we suppose that at 15° C, gc/v = 10~ rs , then 

 if c = 10~ 8 , which is about right for sodium, v = 10'°xg. 

 When v is known, w T e can get n from the equation 



±mnv 2 = JR#. 



If v = 10 5 <7, this equation gives 



7i = 4-4 xlO 3 /^ 2 . 



As g must be less than unity, the chains at this temperature 



