A crystal diffracts a beam of electrons, like a diffraction grating, as they hit

Question

A crystal diffracts a beam of electrons, like a diffraction grating, as they hit it perpendicular to its surface. The crystal spacing is 0.18 nm, and the first maximum scattering occurs at 80° relative to the normal to the surface.
Given:

e = 1.60 × 10-19 C, melectron = 9.11 × 10-13 kg, h = 6.626 × 10-34 J s

(Hint: 2d*Sin() = m , E = h*f = h c / )

(a) What is the wavelength of the electrons?

(b) What potential difference accelerated the electrons if they started from rest?

Please show IN DEPT conceptual plan to solve this problem. Thanks

Explanation / Answer

from the Bragg's law

2d*Sin() = m ,

= 2d*Sin() /m = 2 (0.18 * 10^-9 m) sin80/1 = 0.3545 * 10^-9 m

(b)

= h/sqrt 2m qV

^2 = h^2/ 2mqV

V = h^2/ 2m q ^2

= ( 6.63 * 10^-34 Js)^2/ 2( 9.1 * 10^-31)( 1.6 * 10^-19 ) (  0.3545 * 10^-9 m)^2

=1.81 V

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