X rays of wavelength 2.63 A were used to analyze a crystal....

X rays of wavelength 2.63 A were used to analyze a crystal. The angle of first-order diffraction $(n=1$ in the Bragg equation) was $15.55^{\circ} .$ What is the spacing between crystal planes, and what would be the angle for second-order diffraction $(n=2) ?$

Key Concepts

Crystal Plane Spacing

Crystal plane spacing, denoted as d in Bragg's Law, refers to the distance between parallel planes of atoms within a crystal lattice. This parameter is key to understanding the internal structure of a crystal since variations in d can affect the diffraction pattern. By measuring diffraction angles and knowing the wavelength of the X-rays, one can use Bragg's Law to compute the spacing between these planes, which in turn provides insight into the arrangement of atoms in the material.

Diffraction Order

The diffraction order, represented by the variable n in Bragg's Law, specifies the sequence of constructive interference resulting from the reflection of X-rays off crystal planes. First-order diffraction (n = 1) is typically the most intense and easiest to observe, while higher-order diffractions (n > 1) occur at larger angles or may have lower intensity. Understanding the order of diffraction is crucial for correctly interpreting diffraction patterns and solving for crystal structure details.

Bragg's Law

Bragg's Law is a fundamental principle in the field of X-ray crystallography that relates the wavelength of electromagnetic radiation to the diffraction angle and the spacing between crystal planes. It states that n? = 2d sin?, where n is an integer representing the order of diffraction, ? is the wavelength, d is the distance between the crystal planes, and ? is the diffraction angle. This law provides the basis for determining distances at the atomic scale within a crystal structure.

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