A coherent beam of 1.937 eV photons is incident on a double slit. A screen is L

Question

A coherent beam of 1.937 eV photons is incident on a double slit. A screen is L = 1.8 m away from the source and the width of each slit is a = .010 mm. This creates an interference/diffraction pattern such that the second interference maxima is y2 = 46 mm from the center line.

If we wanted to duplicate this interference/diffraction pattern with monoenergetic electrons of mass me = 9*10-31 kg,
what would the kinetic energy of one of these electrons have to be? ________ eV


I've got that the momentum is 1.033E-27 J*s/m and I think the correct equation is KE= (p^2)/(2m) but nothing I do is getting the correct answer.

Can anyone help?

Explanation / Answer

Given distance between screen and slit is   L = 1.8 m distance between second maxima and central line is   y = 46 mm = 0.046 m width of slit is     D = 0.01 mm positionof second maxima is                   y = L tan                  0.046 = 1.8 m tan                            = 1.4639 o        condition for maxima is             sin   = m / D              sin 1.4639 = 2 / 0.01*10-3 m      wave length of incident  beam is                 = 1.27736*10-7 m     momentum                 P = h /     here   h is plancks constant                 P = 6.635*10-34 Js / 1.27736*10-7 m                     = 5.194*10-27 kg m/s        kinetic energy of electron is                K. E =  P 2 / 2m                        = ( 5.194*10-27 kg m/s   ) 2 / 2 ( 9.11*10-31 )                         = 1.48*10-23 J                         = 9.254*10-5 e V                                           condition for maxima is             sin   = m / D              sin 1.4639 = 2 / 0.01*10-3 m      wave length of incident  beam is                 = 1.27736*10-7 m     momentum                 P = h /     here   h is plancks constant                 P = 6.635*10-34 Js / 1.27736*10-7 m                     = 5.194*10-27 kg m/s        kinetic energy of electron is                K. E =  P 2 / 2m                        = ( 5.194*10-27 kg m/s   ) 2 / 2 ( 9.11*10-31 )                         = 1.48*10-23 J                         = 9.254*10-5 e V                                     

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