Solid State · Chemistry · JEE Advanced

In a metal deficient oxide sample, $\mathbf{M}_{\mathbf{x}} \mathbf{Y}_2 \mathbf{O}_4$ ( $\mathbf{M}$ and $\mathbf{Y}$ are metals), $\mathbf{M}$ is present in both +2 and +3 oxidation states and $\mathbf{Y}$ is in +3 oxidation state. If the fraction of $\mathbf{M}^{2+}$ ions present in $\mathbf{M}$ is $\frac{1}{3}$, the value of $\mathbf{X}$ is _______ .

Atom $\mathrm{X}$ 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

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

The arrangement of X^$$-$$ ions around A⁺ ion in solid AX is given in the figure (not drawn to scale). If the radius of X^$$-$$ is 250 pm, the radius of A⁺ is

A compound M_pX_q has cubic close packing (ccp) arrangement of X. Its unit cell structure is shown below. The empirical formula of the compound is

The packing efficiency of the twodimensional square unit cell shown below is

Atoms of metals $\mathrm{x}, \mathrm{y}$, and $\mathrm{z}$ form face-centred cubic (fcc) unit cell of edge length $\mathrm{L}_{\mathrm{x}}$, body-centred cubic (bcc) unit cell of edge length $\mathrm{L}_y$, and simple cubic unit cell of edge length $\mathrm{L}_z$, respectively.

If $\mathrm{r}_{\mathrm{z}}=\frac{\sqrt{3}}{2} r_{\mathrm{y}} ; \mathrm{r}_{\mathrm{y}}=\frac{8}{\sqrt{3}} \mathrm{r}_{\mathrm{x}} ; M_{\mathrm{z}}=\frac{3}{2} M_{\mathrm{y}}$ and $M_{\mathrm{z}}=3 M_{\mathrm{x}}$, 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.
$\mathrm{r}_{\mathrm{x}}, \mathrm{r}_{\mathrm{y}}$, and $\mathrm{r}_{\mathrm{z}}$ are atomic radii of metals $\mathrm{x}, \mathrm{y}$, and $\mathrm{z}$, respectively.]

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).

The CORRECT statement(s) for cubic close packed (ccp) three dimensional structure is (are) :

If the unit cell of a mineral has cubic close packed (ccp) array of oxygen atoms with m fraction of octahedral holes occupied by aluminium ions and n fraction of tetrahedral holes occupied by magnesium ions, m and n, respectively, are

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 $$\,\,\left( {{{number\,\,of\,\,anions} \over {number\,\,of\,\,cations}}} \right)\,\,$$ in $$Z$$ is ___________.

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

The number of hexagonal faces that are present in a truncated octahedron is ____________.

A compound AB has rock salt type structure. The formula weight of AB is 6.023 Y amu, and the closest A - B distance is Y^1/3 nm, where Y is an arbitrary number
(a) Find the density of the lattice
(b) If the density of lattice is found to be 20 kg m^-3, then predict the type of defect