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A physicist wants to prove that electrons can behave as waves by observing a diffraction pattern...

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Physics

A physicist wants to prove that electrons can behave as waves byobserving a diffraction pattern when a beam of electrons hits ametallic crystal of atomic spacing d. After accelerating theelectrons from rest with an applied voltage V1, a strong peak inthe scattering is seen in the first order at an angle θ1 from thesurface. She then doubles the voltage and observes as strongfirst-order peak at a different angle θ2 , again confirming thewave nature of the electrons.

a) What is the ratioλ2/λ1 of the electron wavelength (express in3 sig figs)? Here λ1 is the deBroglie wavelength for V1 and λ2 isthe same with double the voltage.

b) If θ1 = 60.0 degrees, what is θ2 ? (deg)

c) If the speed of the electrons is 4.67 x 106 m/s for θ1 = 60.0degrees, what is the crystal spacing d? (nm)

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