possibilities of Future Development 125 



tion, after careful preliminary studies, both theoretical and ex- 

 perimental, extending over several years. 



It is easy to see that the proton microscope should have, in 

 principle, a resolution limit appreciably better than any uncor- 

 rected electron microscope. The de Broglie wavelength A of a 

 particle of mass m and charge e which has dropped through a 

 potential V and has acquired a velocity v is, by equation (12) 

 on p. 15 



^__ h _ h 



mv \/2meV 



and is, therefore, for particles of equal charge and equal ac- 

 celerating voltage, inversely proportional to the square root of 

 the masses. The mass ratio of protons and electrons is 1840, 

 and its square root 42.9. 



Introducing A instead of V in equation (24) on p. 39, the 

 resolution limit as determined by spherical aberration and dif- 

 fraction, without chromatic error becomes 



13 1 



c/sA= l.HC^A^f 



This formula is valid for protons as well as for electrons. Thus 

 if it were possible to use in the proton microscope objective lenses 

 of the same quality and strength as in the best electron micro- 

 scopes, that is to say with the same values of C and /, and at the 

 same voltage V, the middle factor would give an advantage of 



3 



42.9* = 16.8 in favor of the proton microscope. But not all of 

 this huge gain can be realized. It is not possible to use magnetic 

 lenses for protons, as for the same strength, at the same accel- 

 erating potential, the magnetic fields would have to be 42.9 

 times stronger. Therefore, proton microscopes can be operated 

 only electrostatically. But the spherical aberration coefficient of 

 the best electrostatic lenses is about ten times larger than for 

 the best magnetic lenses, so that the gain is reduced by a factor 



of about 10* = 1.78 to about 9.5. Moreover, it will be necessary 



