WAVELENGTHS OF CONTROLLED HIGH-SPEED ELECTRONS 331 



The de Broglie Waves 



The modern electron microscope or micrographic projector is a 

 device that uses matter waves instead of light waves to make details of 

 structure photographable. High-velocity electrons, according to the 

 de Broglie theory of quantum dynamics, have associated with them 

 so-called matter waves. The lengths of these waves are associated 

 with the momentum of the particle according to the fundamental ex- 

 perimentally verified* relation 



h 

 X = — 



mv 



in which the wavelength X becomes less as the velocity v of the electron, 

 of mass m, increases, h is Planck's constant. 



If the velocity of the electron is small we may use the rest mass mo 

 for m. Thus an electron of rest mass m = 9.11 X 10 -28 gram moving 

 with a velocity of 5.94 X 10 8 cm/sec has associated with it a wave- 

 length equal to 1.22 X 10~ 8 cm. 



Wavelengths of Controlled High-Speed Electrons 



If an electron is placed in a uniform electric field, as for instance the 

 field between two oppositely charged parallel condenser plates, in a 

 vacuum tube, it will move toward the positively charged plate and gain 

 kinetic energy. This gain in energy is proportional to the difference of 

 potential V to which the plates are charged. As the electron emerges 

 from the electric field it will have a velocity v given by §m v 2 = eF/300, 

 if v is not too large. On substituting this relation in the de Broglie 

 equation it is found that 



h /150 in 8 



x = I V e =V^' 10 cm 



\ 150 m 



The wavelength associated with an electron after the electron has moved 

 down a potential gradient of 150 volts is as small as 1 A, or it may be 

 said that a 1-volt electron has a wavelength equal to 12.3 A. This 

 result is correct to 0.5 per cent if the velocities of the electrons are not 

 too high. 



In order to use the wavelengths associated with very high-speed 

 electrons, of the order of 50 kilovolts (50,000 ev) or more, the relativity 



* Experimental confirmation of de Broglie's theory was first achieved in 1927 by 

 Davisson and Germer of the research laboratories of the Bell Telephone Company, 

 New York. 



