Physics

Problem

For electrons diffracted by a crystal having interplanar spacing

d

, it is required to obtain a general relationship between the accelerating potential

V

and the glancing angle

\theta

of the first-order maximum. a. (i) Write the expression for the de Broglie wavelength of an electron in terms of

V

. b. (ii) State the condition for the first-order constructive scattering from a set of parallel crystal planes separated by

d

. c. (iii) Combine the two expressions obtained in parts (i) and (ii) to derive a formula that relates

\sin\theta

directly to the accelerating potential

V

and the spacing

d