There are three cubic unit cells for the atomic solids, namely, simple cubic, body–centered cubic an — Physical Chemistry — Kinetics Chemistry Question
Crystal Packing
There are three cubic unit cells for the atomic solids, namely, simple cubic, body–centered cubic and face–centered cubic. They are illustrated in the following figures:
How many nearest neighbour atoms are in each packing, respectively?
Model Answer
Simple cubic: 6, body–centred cubic: 8 and face–centred cubic: 12
In each packing, the packing efficiency is defined by
volume occupied by spheres in the unit cell / volume of the unit cell = fv
What is the value of fv in each type of packing, respectively?
Model Answer
For simple cubic, a = 2 r,
fv = (4/3 π r^3) / a^3 = 52.4%
For body–centred cubic, √3 a = 4 r,
fv = 2 × (4/3 π r^3) / a^3 = 68%
For face–centred cubic, √2 a = 4 r,
fv = 4 × (4/3 π r^3) / a^3 = 74%
Silver crystallizes in a cubic closest packed structure, i.e. face–centered cubic. The radius of a silver atom is 144 pm. Calculate the density of silver.
Model Answer
√2 a = 4 r, a = 407 pm
d = (107.9 × 4) / [6.02 × 10^23 × (407 × 10^-10)^3] = 10.6 g cm^-3
X–ray diffraction is commonly used for the determination of crystal structures. In one such determination, the emitted X rays were diffracted by a LiF crystal (d = 201 pm), and the first–order diffraction was detected at an angle of 34.68°. Calculate the wavelength of the X–ray emitted by the metal.
Model Answer
λ = 2 d sinθ
λ = 2 × 201 × sin(17.34°) = 229 pm