A beam consisting of 50 eV electrons (electron mas...

A beam consisting of 50 eV electrons (electron mass 9.11 *10^-31 kg) is incident on a thin wafer of a crystal with layerspacing 4.6 Angstroms. Surprisingly we find that theelectrons, which are particles, are scattered in such a way as toform an interference pattern identical to that of a wave. What will be the distance between central interference maxima at adistance of 18 cm from the wafer?

Answers ( 1 )

  1. camille ennis
    camille ennis
    x.x?=sp;
      
    ANS)
                        THE ENERGY OF 50EV ELECTRON BEAM IN JOULES IS
                        
                                                                          =   50 * 1.6 *10^-19 J
                                                                         
                                                                           = 80 *10^-19 J
                           
                             AS THE ELECTRON BEAM HAS WAVE NATURE THE WAVE LENGTH
         OF THE MATTER WAVE CAN BE DETERMINED BY THE DEBROGLE RELATION
                                                      ? = h/(? 2 m E)
                                                                                            h= planks constant
                                                                                             m= rest mass of the electron
                                                                                             E = energy of the electron beam
                                                                                             ? = wavelength.
                            
                                                    ?   = 6.626 * 10 ^ -34 / ? (2 * 9.1 *10 ^ -31 * 80 * 10^ -19 )
          
                                                             = 1.7355 * 10 ^-10 m
       
                       considering this wave lenght of the electron beam falling on double slit using the
                                                                                        relation
                                                                       
                                                                X = n ? D / 2 d               ------ EQ - 1
                                                                                    
                                                                         X   IS DISTANCE OF THE MAXIMA
                                                                                         FROM THE MEAN POSITION    ?  
                                                                                    
                                                                         n IS THE ORDER OF THE MAXIMA 1
                                                                                        
                                                                  D IS THE DISTANCE OF THE SCREEN FROM
                                                                                    THE WRAFER OF THE CRISTAL  18 c m
                                
                                        2d DISTANCE BETWEEN LAYERS OF CRYSTAL 4.6 A
                                                
                                    SUBSTITUTING THIS VALUES IN   -- EQ - 1
      
                                                            X =    1.7355 * 10^ -10 * 0.18 / 4.6 * 10 ^ -10
            
                                                                   = 6.7910 cms
                                   here we took n = 1 as we need the distance of the first maxiam from the
                                                                                                      centre
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