Pure gold crystallizes in a face-centered cubic unit cell with an edge length of 4.08 Å. The alloy called 18-karat gold consists of 75% Au, 8.0% Ag, and 17% Cu by mass. What are the subscripts in the empirical formula of 18-karat gold (Au(x)Ag(y)Cu(z)) to two significant digits?

(a) Magnesium (Mg) has a hexagonal close-packed (HCP) crystal structure with the lattice parameter of a = 0.321 nm and c= 0.521 nm and the atomic radius is 0.173 nm. (i) What is the number of atoms per unit cell in HCP structure? (ii) Determine the atomic packing factor of the Mg unit cell. (iii) Is Mg containing an ideal atomic packing factor? You may justify your answer by evaluating the HCP c/a ratio. Subsequently, will slip be harder in Mg compared to the ideal HCP structure? Justify your answer.

a) Draw rock salt unit cell of NaCl and give the coordinates (u,v,w) describing the positions of all the atoms in such a unit cell. b) Calculate the structure factor |F_hkl|^ 2 for such a unit cell for x-ray scattering from a given set of crystallographic planes (hkl). c) Which reflection peaks have the lowest and highest intensities and why

In the early days of X-ray crystallography there was an urgent need to know the wavelengths of X-rays. One technique was to measure the diffraction angle from a mechanically ruled grating. Another method was to estimate the separation of lattice planes from the measured density of a crystal. The mass density of NaCl is 2.17 g cm−3 and the (100) reflection using radiation of a certain wavelength occurred at 6.0°. Calculate the wavelength of the X-rays.

A metal crystallizes in the face-centered cubic crystal structure with a unit cell edge of 3.52 x 10 -8 cm.The density of the metal is 8.90 g/cc. (a) What is the mass, in grams, of a single atom of this element? (b) What is the atomic weight of the element (g/mol). (c) What is the radius, in cm, of an atom of the element?

The density of platinum is 21.45 g/cm3.  It crystallizes in a fcc lattice. Calculate its metallic radius.