536 



Table 654 

 CATHODE RAYS 



Prepared by W. W. Nicholas, Bur. Standards 

 Cathode rays are swiftly moving electrons, and thus are of the same nature as /3 rays 

 (see tables on radioactivity, pages 526 to 528). They are produced in gas discharge tubes. 

 At comparatively low pressures the cathode rays thus produced have a nearly uniform 

 velocity. Free electrons are emitted from hot bodies (Table 667), especially if the heated 

 substance is coated with barium, calcium, or strontium oxide (Wehnelt cathode). These 

 electrons can be given any desired speed if the heated substance (usually in the form of a 

 wire) be enclosed in an evacuated tube and the difference of potential (V) applied between 

 the wire (cathode) and another electrode (anode, anticathode, or target). The speed (v) 

 of the cathode rays, expressed as a fractional part (/3) of the speed of light (p-=v/c, 

 where c is the speed of light), when they have fallen through the entire potential differ- 

 ence, is given by the formula (corrected for the relativity change of mass) 



F= 5 o8.H (i_/3=)i _i \ 

 where V is in absolute kilovolts. The equivalent power series, 



F= 254.O ]/3 2 +a)/3 4 +(f)/3«+(§f)/3 8 \ t 



is useful for calculations at low and intermediate speeds (error is about 1% for /3 = 0.60, 

 using terms given here). A tabulation of the corresponding values of V (absolute kilo- 

 volts) and /3 follows. An electron speed of 0.2 cm/sec. is spoken of, e.g., as a 10.5 kilovolt 

 electron, or as having an equivalent voltage of 10.5 kv. 



Cathode rays whose direction of motion is perpendicular to the direction of a uniform 

 magnetic field (H) describe a circular path of radius (r) according to the formula (cor- 

 rected for relativity change of mass of electron) 



Hr=i6Q5"!/3(i-/3 2 )n 

 where H is expressed in gauss and r in cm. 



When they impinge on matter, cathode rays are deflected from their original direc- 

 tion of motion. These deflections grade all the way from 180 "reflections" to the 

 " diffusion " corresponding to deflections through very small angles. The large-angle 

 deflections are ordinarily comparatively infrequent. However, when the substance struck 

 by the cathode rays is crystalline, certain directions may be preferred by the deflections. 

 Here the beam of cathode rays behaves as though it consisted of a train of waves of 

 wave length Xc = 0.02428//3, where \e is in Angstroms. The preferred directions for the 

 " reflected " cathode ray beams may be calculated from the Bragg formula (see Siegbahn's 

 "X-ray Spectroscopy"). The simple Bragg formula is quite limited in application here, 

 however, since refraction in the crystal is very appreciable for the cathode ray beams. 

 In general, the cathode rays which have been deflected by matter will have lost speed, but 

 the rays which have undergone these " preferred " deflections remain of the same speed 

 as the primary cathode beam. 



Cathode rays lose speed on penetrating matter. The losses of speed by individual 

 cathode particles grade from complete stoppage to no loss of speed. The majority of 

 the cathode particles, however, lose speed according to the relation (Thomas-Whiddington- 



Bohrlaw) (*-?= ax 



where /3 is the initial speed, and /3 the speed after traversing a path length x in the 

 material (x to be measured in cm along the actual curved path), and a is a constant 

 roughly equal to 6.5P where p is the density of the material in g/cm 3 . A convenient form 

 for the expression is the following. Note that the two forms are not equivalent except at 

 very low speeds (experiment has not yet decided between the two) : 



Vo 2 -V 3 =bx 

 where V and V are the initial and final "equivalent voltages" (see above) of the 

 cathode rays, in kv, and b is a constant roughly equal to 40 X io*p. A tabulation of experi- 

 mental values of a and b for various materials follows : 

 Smithsonian Tables 



