-64. The distance between the 111 surface of silver and the...

-64. The distance between the 111 surface of silver and the second layer of atoms is $235 \mathrm{pm}$, the same as in the bulk. If electrons with a kinetic energy of $8.77 \mathrm{eV}$ strike the surface, will an electron diffraction pattern be observed?

Key Concepts

Crystal Lattice Spacing

Crystal lattice spacing refers to the regular, periodic distance between atomic planes in a crystalline material. When the wavelength of incident particles is comparable to these spacings, interference effects such as diffraction occur, making lattice spacing a key parameter in analyzing and interpreting diffraction patterns.

Kinetic Energy and Momentum Relation

The relation between kinetic energy and momentum (expressed as p = ?(2mE) for non-relativistic particles) is crucial because it underpins the calculation of the de Broglie wavelength. This relationship allows us to determine whether the electron’s wavelength is on the same order of magnitude as the interatomic spacing needed for diffraction to occur.

De Broglie Wavelength

The de Broglie wavelength is the wavelength associated with any moving particle, calculated from its momentum. For electrons, a lower kinetic energy corresponds to a longer wavelength, making it comparable in scale to the spacing between atomic planes and thus capable of producing observable diffraction effects.

Electron Diffraction

Electron diffraction is the phenomenon where electrons, exhibiting wave-like properties, display interference effects when they scatter from a periodic atomic structure. This interference produces distinct diffraction patterns that provide insight into the structure and spacing of the atoms in a crystal.

Bragg’s Law

Bragg’s law describes the condition for constructive interference when waves are scattered by a crystal lattice. According to the law, the path difference between waves reflected from successive atomic planes must be an integer multiple of the wavelength, establishing a direct relationship between the wavelength of the electrons and the spacing of the crystal planes.

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