552 Microscopy /29 : 8 



Electron microscopes focus electrons instead of light beams. The 

 electrons may be considered as waves in the same sense as electromag- 

 netic waves, or may be treated as rays of particles just as light may be. 

 The significant difference is that electron microscopes can resolve 

 separate images of points so close together that their images would fuse 

 in the conventional optical microscopes. The theory of the operation 

 of the electron microscope, and indeed its physical structure, are in 

 every way analogous to those of a light microscope. However, the 

 resolution of the electron microscope is far greater. The higher resolu- 

 tion is possible because the electron wavelength is much shorter than the 

 wavelength of a visible photon. 



As discussed in the last chapter, quantum mechanics represents an 

 electron by a packet of waves of proper phases and slightly varying 

 frequency. The wave velocity varies with the frequency. The com- 

 ponent waves cancel except in a small region, and this region moves 

 with a velocity called a group velocity which is different from the wave 

 velocity. Modern quantum mechanics shows that v, the average 

 frequency of the electron wave, and A, its average wavelength, can be 

 represented by the expressions 



E = hv — mc 2 



h 



p = mv = - 

 A 



where E is the total energy of the electron, p is its momentum, v is its 

 velocity, h is Planck's constant, c is the velocity of light in a vacuum, 

 and m is the (relativistic) mass of the electron moving with velocity v. 

 (For computing A and v for electrons within an electron microscope, m is 

 approximately the same as m Q , the rest mass. Hence, the frequency is 

 constant, and the change in frequency is negligible.) 



If an electron is accelerated by passing through a potential difference, 

 V, it gains momentum 



p = V2mVe 

 and hence, has a wavelength 



A- * 



V2mVe 



For a potential difference of 50 kilovolts (a typical value for an electron 

 microscope), the electronic wavelength is 



A = 0.08 A 



Even if the lenses are so poor that the resolution obtained is 1 00 times 



