Question

If a strong diffraction peak is observed when electrons are incident at an angle i from the normal to the crystal planes with distance d between them (see figure), de Broglie wavelength λ_dB of electrons can be calculated by the relationship (n is an integer)

Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see figure).

(a) dcosi = nλ_dB 

(b) dsini = nλ_dB

(c) 2dcosi = nλ_dB 

(d) 2dsini = nλ_dB.

Answer 1

(c) : Bragg’s relation nλ = 2dsinθ for having an intensity maximum for diffraction pattern.

But as the angle of incidence is given, nλ = 2dcosi is the formula for finding a peak.