X rays of wavelength 0.0850 nm are scattered from the atoms...

X rays of wavelength 0.0850 nm are scattered from the atoms of a crystal. The second-order maximum in the Bragg reflection occurs when the angle $\theta$ in Fig. 36.22 is 21.5$^\circ$. What is the spacing between adjacent atomic planes in the crystal?

Key Concepts

Bragg's Law

Bragg's Law is a fundamental equation in crystallography that relates the wavelength of incident waves (such as x-rays) to the angle of incidence and the spacing between atomic planes in a crystal. It is expressed as n? = 2d sin?, where n is the order of the diffraction maximum, ? is the wavelength, d is the interplanar spacing, and ? is the angle of incidence. This law is crucial for determining the structure of crystals by analyzing the diffraction patterns produced when x-rays interact with the lattice.

Interplanar Spacing

Interplanar spacing refers to the distance between adjacent parallel planes of atoms within a crystal. It is an important parameter that influences the diffraction pattern observed in x-ray crystallography. By applying Bragg's Law, one can calculate the spacing between these atomic planes from the measured angles and known wavelengths, providing insight into the crystal's structure.

Diffraction Order

The diffraction order, denoted by the integer n in Bragg's Law, indicates the sequence of the observed peak corresponding to multiple wavelengths fitting into the path difference between waves reflected from successive atomic planes. Higher orders correspond to larger multiples of the wavelength and provide additional information about the crystal's periodic structure, although typically the first few orders are the most relevant in experiments.

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