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?

A compound AB has rock salt type structure. The formula weight of AB is 6.023 Y amu, and the closest AB distance is $Y^{\frac{1}{3}}$ nm, where Y is an arbitrary number. The density of lattice is

The density of mercury is 13.6 g ml^-1. The approximate diameter of an atom of mercury assuming that each atom is occupying a cube of edge length equal to the diameter of the mercury atom is

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.

A metal can be crystallized in both BCC and FCC unit cells whose edge lengths are $2 \mathrm{pm}$ and $4 \mathrm{pm}$ respectively. Then ratio of densities of FCC and BCC unit cells is

A crystalline solid $\mathrm{AB}$ adopts sodium chloride type structure with edge length of the unit cell as $745 \mathrm{pm}$ and formula mass of $74.5 \mathrm{a}.\mathrm{m}.\mathrm{u}$. The density of the crystalline compound is

An element forms ccp lattice with a cell edge length of $400 \mathrm{pm}$. The density of the element is $10 \mathrm{g} {\mathrm{cm}}^{-3}$. The atoms mass of the element will be [Take ${\mathrm{N}}_{\mathrm{A}}=6.02\times {10}^{23}$]

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 = $6.022 \times {10}^{23}, 1 \mathrm{\AA } = 1 \times {10}^{-8} \mathrm{cm}$)

A metal crystallises into two cubic phases fcc and bcc whose unit lengths are $3.5$ and $3.0 \stackrel{°}{\mathrm{A}}$, respectively, the ratio of densities of fcc and bcc is:-
 

A solid has a density of $9\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$ forms face-centred cubic crystals of edge length $200\sqrt{2}$ $\mathrm{pm}$. What is the molar mass of the solid? (Avogadro's constant $\cong 6\times {10}^{23} {\mathrm{mol}}^{-1}$)

At $100°\mathrm{C}$, copper $\left(\mathrm{Cu}\right)$ has $\mathrm{FCC}$ unit cell structure with a cell edge length of $\mathrm{x} \stackrel{\circ }{\mathrm{A}}$. What is the approximate density of $\mathrm{Cu}$ (in $\mathrm{g} {\mathrm{cm}}^{-3}$) at this temperature? (Atomic mass of $\mathrm{Cu}=63.55 \mathrm{u}$)

The number of unit cells in $100 \mathrm{g}$ of FCC crystal with density $10 \mathrm{g} {\mathrm{cm}}^{-3}$ and cell edge of $200 \mathrm{pm}$, is
 

The number of atoms in $100 \mathrm{g}$ of an FCC crystal with density $\mathrm{d}=10 \mathrm{g}/{\mathrm{cm}}^3$ and cell edge equal to $100 \mathrm{pm}$ is equal to:

Sodium crystallises in a $\mathrm{BCC}$ arrangement with the interfacial separation between the atoms at the edge $53 \mathrm{pm}$. The density of the solid is

Iron exhibits $\mathrm{BCC}$ structure at room temperature. Above $900°\mathrm{C}$, it transforms to $\mathrm{FCC}$ structure. The ratio of density of iron at room temperature to that at $900°\mathrm{C}$ (assuming molar mass and atomic radius of iron remains constant with temperature) is