All Problems

Wave Properties of particles. Schrodinger Equation.

Problem 6.61

A narrow beam of monoenergetic electrons falls normally on the surface of a Ni single crystal. The reflection maximum of fourth order is observed in the direction forming an angle \(\theta=55^{\circ}\) with the normal to the surface at the energy of the electrons equal to \(T=180 \mathrm{eV} .\) Calculate the corresponding value of the interplanar distance.

Reveal Answer
d=πk/2mTcos(θ/2)=0.21nm, where k=4d=\pi \hbar k / \sqrt{2 m T} \cos (\theta / 2)=0.21 \mathrm{nm}, \text { where } k=4