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Wave Properties of particles. Schrodinger Equation.

Problem 6.62

A narrow stream of electrons with kinetic energy \(T\) \(=10 \mathrm{keV}\) passes through a polycrystalline aluminium foil, forming a systeun of diffraction fringes on a screen. Calculate the interplanar distance corresponding to the reflection of third order from a certain system of crystal planes if it is responsible for a diffraction ring of diameter \(D=3.20 \mathrm{~cm} .\) The distance between the foil and the screen is \(l=10.0 \mathrm{~cm}\)

Reveal Answer
 6.62. d=πℏk/2mTsin⁡θ=0.23±0.04nm, where k=3 and the  angle θ is determined by the formula tan⁡2θ=D/2l . \begin{aligned} &\text { 6.62. } d=\pi \hbar k / \sqrt{2 m T} \sin \theta=0.23 \pm 0.04 \mathrm{nm}, \text { where } k=3 \text { and the }\\ &\text { angle } \theta \text { is determined by the formula } \tan 2 \theta=D / 2 l \text { . } \end{aligned}
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