Calculations Involving Unit Cell Dimensions

Calcium crystallizes in a face centred cubic unit cell with a $\text{=}\text{0}\text{.560}\text{nm}\text{.}$  The density of the metal if it contains 0.1% schottky defects would be:

Copper crystallises in a face-centred cubic lattice and has a density of  $8.930\mathrm{g}{\mathrm{cm}}^{-3}$ at $393 \mathrm{K}.$ The radius of a copper atom is:
[Atomic mass of$\mathrm{Cu}=63.55\mathrm{u},{\mathrm{N}}_{\mathrm{A}}=6.02\times {10}^{23}{\mathrm{mol}}^{-1}]$

Iron has a body-centered cubic unit cell of cell edge $286.65 \mathrm{pm}$. The density of iron is $7.87 \mathrm{g} {\mathrm{cm}}^{-3}$. The Avogadro number is

(Atomic mass of iron $=56\hspace{0.17em}\mathrm{g}\hspace{0.17em}{\mathrm{mol}}^{-1}$)

X-rays diffraction studies show that copper crystallizes in an FCC unit cell with cell edge of  $3.6885\times {10}^{-8}\mathrm{cm}.$ In a separate experiment, copper is determined to have a density of  $\text{8}{\text{.92g/cm}}^{\text{3}}$, the atomic mass of copper would be:

In face-centred cubic $\left(\mathrm{FCC}\right)$ and body centred cubic $\left(\mathrm{BCC}\right),$ whose unit cell lengths are $3.5$ and $3.0$ $\mathrm{\AA }$ respectively, a metal crystallises into two cubic phases. What is the ratio of densities of $\mathrm{FCC}$ and $\mathrm{BCC}?$

A unit cell of sodium chloride has four formula units with an edge length of the unit cell $0.564 \mathrm{nm}$. What is the density of sodium chloride?

Copper crystallizes in an FCC unit cell with cell edge of  $3.608\times {10}^{-8}\mathrm{cm}.$ The density of copper is  $\mathrm{8}.92 \mathrm{g}/{\mathrm{cm}}^{\mathrm{3}}$, Calculate the atomic mass of copper.

Ice crystallises in a hexagonal lattice. At the low temperature at which the structure was determined, the lattice constants were $\mathrm{a}=4.53 \mathrm{\AA }$ and $\mathrm{c}=7.41 \mathrm{\AA }$. How many ${\mathrm{H}}_2\mathrm{O}$ molecules are contained in a unit cell? The density of ice is $0.92 \mathrm{g}/\mathrm{cc}$ at $0 °\mathrm{C}.$ A unit cell of ${\mathrm{H}}_2\mathrm{O}$ is shown below:

The density of iron crystal is $8.54 \mathrm{g} {\mathrm{cm}}^{–3}$. If the edge length of unit cell is $2.8 \mathrm{\AA }$ and atomic mass is $56 \mathrm{g} {\mathrm{mol}}^{–1}$, find the number of atoms in the unit cell. (Given: Avogadro’s number = $6.022 \times {10}^{23}, 1 \mathrm{\AA } = 1 \times {10}^{-8} \mathrm{cm}$)

An element with atomic mass $107.9\mathrm{u}$ crystallizes in a FCC cubic lattice with edge length of $408.6 \mathrm{pm}$. Calculate the density of the metal in $\mathrm{a}\times {10}^{3 }{\mathrm{kgm}}^{-3}$.Thus, calculate the value of 'a'.
(${\mathrm{N}}_{\mathrm{A}}=6.022 \times {10}^{23}$)

Lithium metal has a BCC lattice structure with edge length of unit cell is $352 \mathrm{pm}$. Calculate density of the metal in ${\mathrm{gcm}}^{-3}$. (${\mathrm{A}}_{\mathrm{Li}}=7 {\mathrm{gmol}}^{-1}$) 

Calcium metal crystallizes in a FCC cubic lattice with edge length of $0.556 \mathrm{nm}$. Calculate the density of the metal in ${\mathrm{kgm}}^{-3}$.

How can you calculate the atomic mass if density and the dimension of a unit cell are given of an unknown metal? Explain. 

X-ray diffraction studies show that copper crystallizes in an FCC unit cell with cell edge of $3.608 \times {10}^{-8} \mathrm{cm}$. In a separate experiment, copper is determined to have a density of  $8.92 \mathrm{gm} {\mathrm{cm}}^{-3}$. Calculate the atomic mass of copper. 

An element has a body centred cubic (bcc) structure with a cell edge of $288 \mathrm{pm}$. The density of the element is $7.2 \mathrm{gm} {\mathrm{cm}}^{-3}$. How many atoms are present in $208 \mathrm{gm}$ of the element? 

Niobium crystallizes in body centred cubic structure. The density in $8.55 \mathrm{gm}/{\mathrm{cm}}^3$, calculate atomic radius of niobium using its atomic mass $93 \mathrm{u}$. 

Silver crystallizes in FCC lattice. If edge length of the cell is $4.077\mathrm{x}{10}^{-8} \mathrm{cm}$ and density is $10.5 \mathrm{g} {\mathrm{cm}}^{-3}$. Calculate the atomic mass of silver. 

Determine the density of cesium chloride which crystallises in a bcc type structure with the edge length $412.1 \mathrm{pm}$. The atomic masses of $\mathrm{Cs}$ and $\mathrm{Cl}$ are $133$ and $35.5$ respectively.

Copper crystallises into a fcc structure and the unit cell has length of edge $3.61\times {10}^{-8} \mathrm{cm}$. Calculate the density of copper if the molar mass of $\mathrm{Cu}$ is $63.5 \mathrm{g} \mathrm{mol}. (8.92 \mathrm{g} {\mathrm{cm}}^{-3})$

Aluminum crystallizes in a cubic close packed structure. Its metallic radius is $125 \mathrm{mm}$. What is the length of the side of the unit cell?