Diffraction of X rays with l = 131.5 pm occurred at an angle of 25.5 degrees by a crystal of aluminum. Assuming first-order diffraction, what is the interplanar spacing in aluminum? (LO 12.2) (a) 76.4 pm (b) 183.1 pm (c) 305.5 pm (d) 152.7 pm

Bragg's Law relates the wavelength of X-rays to the angle of diffraction and the interplanar spacing in a crystal. It is expressed as nλ = 2d sin(θ), where n is the order of diffraction, λ is the wavelength, d is the interplanar spacing, and θ is the angle of diffraction. This law is fundamental in determining the arrangement of atoms within a crystal structure.

Interplanar spacing (d) refers to the distance between parallel planes of atoms in a crystal lattice. It is a critical parameter in crystallography, influencing how X-rays are diffracted. The value of d can be calculated using Bragg's Law, which helps in identifying the crystal structure and properties of materials.

First-order diffraction occurs when n = 1 in Bragg's Law, indicating the first set of parallel planes that diffract X-rays. This is the simplest case and provides the most direct relationship between the wavelength, angle, and interplanar spacing. Understanding first-order diffraction is essential for accurately calculating the interplanar spacing in crystalline materials.