An electron beam is accelerated across a potential difference and on a thin film containing crystal fragments that are randomly oriented. The apparatus is like the one we used in the experiment we analyzed this semester, except that the circular ring images are formed on a flat screen, rather than on the surface of a spherical bulb. All the crystal fragments have the same interatomic spacing, dnkl = 0.160 nm. (a) If the accelerating potential difference is 2.8 kV, calculate the electron kinetic energy in eV units. (b) Use the result from (a) to find the electron momentum in Ns units. (c) Use the result from (b) to find the electron wavelength in nm units. (d) Calculate the diffraction angle for the first two orders of Bragg diffraction. Do not use the small angle approximation.
An electron beam is accelerated across a potential difference and on a thin
film containing crystal fragments that are randomly oriented. The apparatus
is like the one we used in the experiment we analyzed this semester, except
that the circular ring images are formed on a flat screen, rather than on the
surface of a spherical bulb. All the crystal fragments have the same
interatomic spacing, dnkl = 0.160 nm.
(a) If the accelerating potential difference is 2.8 kV, calculate the electron kinetic energy in eV units.
(b) Use the result from (a) to find the electron momentum in Ns units.
(c) Use the result from (b) to find the electron wavelength in nm units.
(d) Calculate the diffraction angle for the first two orders of Bragg diffraction. Do not use the small angle approximation.
(e) The phosphor screen that displays the circular rings is flat and located 22 cm from where the electron beam interacts
with the crystal fragments. Calculate the diameters of the rings produced for the first two orders of Bragg diffraction.
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