Solid State

The density (in $\mathrm{g\,cm^{-3}}$) of the metal which forms a cubic close packed (ccp) lattice with an axial distance (edge length) equal to 400 pm is _____.

Use: Atomic mass of metal $= 105.6$ amu and Avogadro's constant $= 6\times10^{23}\ \mathrm{mol^{-1}}$

In a metal deficient oxide sample, $\mathbf{M_XY_2O_4}$ (M and Y are metals), M is present in both +2 and +3 oxidation states and Y is in +3 oxidation state. If the fraction of $\mathbf{M^{2+}}$ ions present in M is $\dfrac13$, the value of X is _____.

Atoms of metals x, y, and z form face-centred cubic (fcc) unit cell of edge length $L_x$, body-centred cubic (bcc) unit cell of edge length $L_y$, and simple cubic unit cell of edge length $L_z$, respectively.

If $r_z = \dfrac{\sqrt3}{2}r_y$; $r_y = \dfrac{8}{\sqrt3}r_x$; $M_z = \dfrac32 M_y$ and $M_z = 3M_x$, then the correct statement(s) is(are)

[Given: $M_x$, $M_y$, and $M_z$ are molar masses of metals x, y, and z, respectively. $r_x$, $r_y$, and $r_z$ are atomic radii of metals x, y, and z, respectively.]

Atom X occupies the fcc lattice sites as well as alternate tetrahedral voids of the same lattice. The packing efficiency (in %) of the resultant solid is closest to

Atoms of element X form hcp lattice and those of element Y occupy $\dfrac23$ of its tetrahedral voids. The percentage of element X in the lattice is ______. (Nearest integer)

The distance between $\mathrm{Na^+}$ and $\mathrm{Cl^-}$ ions in solid NaCl of density 43.1 g cm$^{-3}$ is ______ $\times10^{-10}$ m. (Nearest Integer)

(Given : $N_A=6.02\times10^{23}\ \mathrm{mol^{-1}}$)

In a solid AB, A atoms are in ccp arrangement and B atoms occupy all the octahedral sites. If two atoms from the opposite faces are removed, then the resultant stoichiometry of the compound is $\mathrm{A_xB_y}$. The value of $x$ is ______. [nearest integer]

Metal deficiency defect is shown by $\mathrm{Fe_{0.93}O}$. In the crystal, some $\mathrm{Fe^{2+}}$ cations are missing and loss of positive charge is compensated by the presence of $\mathrm{Fe^{3+}}$ ions. The percentage of $\mathrm{Fe^{2+}}$ ions in the $\mathrm{Fe_{0.93}O}$ crystals is ______. (Nearest integer)

The incorrect statement about the imperfections in solids is :

An element X has a body centred cubic (bcc) structure with a cell edge of 200 pm. The density of the element is 5 g cm$^{-3}$. The number of atoms present in 300 g of the element X is ______.

Given : Avogadro constant, $N_A=6.0\times10^{23}$ mol$^{-1}$.

Given below are two statements.

Statement I: $\mathrm{O_2}$, $\mathrm{Cu^{2+}}$, and $\mathrm{Fe^{3+}}$ are weakly attracted by magnetic field and are magnetized in the same direction as magnetic field.

Statement II: NaCl and $\mathrm{H_2O}$ are weakly magnetized in opposite direction to magnetic field.

In the light of the above statements, choose the most appropriate answer from the options given below.

An element M crystallises in a body centred cubic unit cell with a cell edge of 300 pm. The density of the element is 6.0 g cm$^{-3}$. The number of atoms present in 180 g of the element is ______ $\times10^{23}$. (Nearest integer)

Metal M crystallizes into a fcc lattice with the edge length of $4.0\times10^{-8}$ cm. The atomic mass of the metal is ______ g/mol. (Nearest integer)

(Use : $N_A=6.02\times10^{23}$ mol$^{-1}$, density of metal, M = 9.03 g cm$^{-3}$)

Ionic radii of cation A$^+$ and anion B$^-$ are 102 and 181 pm respectively. These ions are allowed to crystallize into an ionic solid. This crystal has cubic close packing for B$^-$. A$^+$ is present in all octahedral voids. The edge length of the unit cell of the crystal AB is _______ pm. (Nearest Integer)

For the given close packed structure of a salt made of cation $\mathbf X$ and anion $\mathbf Y$ shown below (ions of only one face are shown for clarity), the packing fraction is approximately $\left(\text{packing fraction} = \dfrac{\text{packing efficiency}}{100}\right)$

The coordination number of an atom in a body-centered cubic structure is _______. [Assume that the lattice is made up of atoms.]

The cubic unit cell structure of a compound containing cation M and anion X is shown below. When compared to the anion, the cation has smaller ionic radius. Choose the correct statement(s).

Consider an ionic solid MX with NaCl structure. Construct a new structure (Z) whose unit cell is constructed from the unit cell of MX following the sequential instructions given below. Neglect the charge balance.

(i) Remove all the anions (X) except the central one

(ii) Replace all the face centered cations (M) by anions (X)

(iii) Remove all the corner cations (M)

(iv) Replace the central anion (X) with cation (M)

The value of $\left(\dfrac{\text{number of anions}}{\text{number of cations}}\right)$ in Z is ______.

A crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of 400 pm. If the density of the substance in the crystal is $8\ \mathrm{g\,cm^{-3}}$, then the number of atoms present in 256 g of the crystal is $N \times 10^{24}$. The value of $N$ is

A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is 'a', the closest approach between two atoms in metallic crystal will be :