332 COMPOUND AND ELECTRON MICROSCOPES 



expression for mass (m = m /Vl - /3 2 ) must be used. Then 



h 1-P 



m c \ /3 



where = v/c, m = 9.107 X 1CT 28 gram, c = 2.998 X 10 10 cm/sec, 



eV 



and (m — m^c 2 = — - . Thus 



oUU 



12.39 1 



Vv 'Vl + 9.72 X 10 _7 F 



where the wavelength is expressed in angstrom units (10 -8 cm) and V in 

 volts. Thus 60-kilovolt electrons have associated wavelengths equal 

 to 4.88 X 10 -10 cm or 0.0488 A, which is about 100,000 times shorter 

 than the wavelength of visible radiation. 



Resolving Power 

 The resolving power of an optical microscope was defined as 



2N.A. 



— i 



R.P. = cm 



A 



Other things being equal, the resolving power is greater, the smaller the 

 wavelength of light that penetrates the condenser, the object, and the 

 optical lens system. With a numerical aperture equal to 1.00 and with 

 ultraviolet illumination having wavelength 2000 A the resolving power 

 is 100,000 cm -1 . The smallest distance resolved, or the resolution, is 

 therefore 10~~ 5 cm. 



The numerical aperture of a typical commercial electron microscope 

 is of the order of 0.02; using 60-kilovolt electrons (X = 4.88 X 10 _10 cm) 

 a resolution of 1.22 X 10 -8 cm is obtained. If it were possible to con- 

 struct a perfect objective utilizing these short wavelengths we would be 

 able to - produce photographable images of some of the giant organic 

 molecules, or obtain an interpretable image of a calcite crystal having a 



o 



grating space at 20 C of 3.35 A. 



Electron Lenses 



Lenses that are built to refract beams of high-speed electrons are called 

 electron lenses. They are either electrostatic- or magnetic-field lenses. 



These electron lenses simulate optical lenses in that they may be 

 designed to diverge or converge a stream of electrons. Just as a beam 

 of light can be deviated from its path at the boundary of an air-glass 



