Electrons are accelerated through a potential difference of 125kV and pass throu

Question

Electrons are accelerated through a potential difference of 125kV and pass through a nickle crystal with a lattice spacing of 2.03 Angstroms. They then are shot toward a phosphorescent screen 50 cm away.

What is the Broglie frequency and wavelength of these electrons?

What is observed on the phosphorescent screen?

Please help. I am having a hard time determining the velocity of these electrons. I know that the electrons are moving at relativistic speeds, but I am not certain how to solve for that. Please help!

Explanation / Answer

potential difference V = 125 kV kinetic energy of electrons is                 K.E = q V here   q is charge on electron                        = 125 keV                      = 125 *1.6*10-16 J    moment of electron                   P = 2 m E                       = 2(9.11*10-31 kg ) ( 125*1.6*10-19 J )                       = 6.0365*10-24kg m/s     debroglie wave length            = h / P                 = ( 6.625*10-34 Js ) / ( 6.0365*10-24                 = 1.097*10-10m debroglie frequency           =   c /               = ( 3*108 ) / ( 1.097*10-10 )               = 2.734*1018Hz    Scintillation is observed . Scintillation is a flash of light produced in a transparent material by an ionization event.

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