A scanning electron microscope is used to look at cell structurewith 10-nm resol

Question

A scanning electron microscope is used to look at cell structurewith 10-nm resolution. A beam of electrons from a hot filament is accelerated with a voltage of 15 kV and then focused to a small spot on the specimen.
(a) What is the wavelength in nanometers of the beam of incoming electrons?
(b) If the size of the focal spot were determined only by diffraction, and if the diameter of the electron lens is one fifth the distance from the lens to the specimen, what would be the minimum separation resolvable on the specimen?
Hint: Recall Rayleigh’s criterion, a sin ?? = 1.22 ?o. (In practice, theresolution is limited much more by aberrations in the magneticlenses and other factors.)

Explanation / Answer

A  beam of electrons from a hot filament is accelerated with a voltage of 15 kV kinetic energy of electrons is                    ( 1/2) m v 2 = q V    speed of electron                            v   = 2 q V / m     charge on electron q = 1.6 *10 -19 C     mass of an electron   m = 9.1*10-31 kg    So speed of electron is                           v = 2(1.6*10-19 C) (15*103 ) / ( 9.1*10-31 kg )                               = 7.262*107 m/s   wave length of the beam of incoming electrons                           = h / mv                               = ( 6.625*10-34 )   / ( 9.1*10-31 ) ( 7.262*107 )                               = 1.0025 nm   ______________________________________________________ Resolution of electron microscopr                     = 10 nm     resolution of microscope                    = 1.22 / 10nm                    = 1.22* 1.0025 nm / 10 nm                        = 0.122305 rad  

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