The Solid State

In a metal deficient oxide sample, \({M}_{X}{Y}_{2}{O}_{4}(M\) 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 \({M}^{2+}\) ions present in \(M\) is \(\frac{1}{3}\), the value of \(X\) is _______.

JEE Advanced 2024, Paper-1]

In a metal deficient oxide sample, M_XY₂O₄(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 M²⁺ ions present in M is \(\frac{1}{3}\), the value of X is _______.

[JEE Advanced 2024, Paper-2]

In a metal deficient oxide sample, \({M}_{X}{Y}_{2}{O}_{4}(M\) 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 \({M}^{2+}\) ions present in \(M\) is \(\frac{1}{3}\), the value of \(X\) is _______.

[JEE Advanced 2024, Paper-2]

Which of the following is not a semiconductor?

Ga (atomic mass \( 70 \mathrm{u} \) ) crystallizes in a hexagonal close packed structure. The total number of voids in \( 0.581 \mathrm{~g} \) of \( \mathrm{Ga} \) is__________ \( \times 10^{21} \). (Round off to the Nearest Integer). [Given : \( \left.\mathrm{N}_{\mathrm{A}}=6.023 \times 10^{23}\right] \)

[JEE Main 2021, 16 Mar (Shift 2)]

A compound is formed by two elements \(X\) and \(Y\). The element \(Y\) forms cubic close packed arrangement and element X occupies one third of the tetrahedral voids. What is the formula of the compound?

[JEE Main 2023, 6 Apr (Shift 1)]

Sodium metal crystallizes in a body centred cubic lattice with unit cell edge length of 4 Å.The radius of sodium atom is _____\(\times 10^{-1}\) Å (Nearest Integer)

[JEE Main 2023, 13 Apr (Shift 2)]

In a binary compound, atoms of element \( \mathrm{A} \) form a hcp structure and those of element M occupy \( 2 / 3 \) of the tetrahedral voids of the hcp structure. The formula of the binary compound is

Iron oxide \(FeO\), crystallises in a cubic lattice with a unit cell edge length of 5.0 Å. If density of the \(FeO\) in the crystal is \(4.0 g cm ^{-3}\), then the number of \(FeO\) units present per unit cell is______ (Nearest Integer)

Given: Molar mass of Fe and \(O\) is 56 and 16 g/mol respectively
\({N}_{A}=6.0\times {10}^{23}mo{l}^{-1}\)

[JEE Main 2023, 30 Jan (Shift 2)]

A hard substance melts at high temperature and is an insulator in both solid and in molten state. This solid is most likely to be a/an

An element crystallises in a face-centred cubic (fcc) unit cell with cell edge a. The distance between the centres of two nearest octahedral voids in the crystal lattice is

[JEE Main 2020, 5 Sep (Shift 2)]

Which of the following expressions is correct in case of a \(CsCl\) unit cell (edge length'a')?

[JEE Main 2023, 15 Apr (Shift 1)]

The correct relationship between unit cell edge length ' \(a\) ' and radius of sphere ' \(r\) ' for face-centred and body centred cubic structures respectively are:

[JEE Main 2023, 10 Apr (Shift 2)]

A metal M forms hexagonal close-packed structure. The total number of voids in \(0.02 \mathrm{~mol}\) of it is ............\(\times 10^{21}\)(Nearest integer). (Given \(\mathrm{N}_{\mathrm{A}}=6.02 \times 10^{23}\) )

[JEE Main 2023, 29 Jan (Shift 2)]

A cubic solid is made up of two elements \(X\) and \(Y\). Atoms of \(X\) are present on every alternate corner and one at the center of cube. Y is at \(\frac{1}{3}\) of the total faces. The empirical formula of the compound is

A diatomic molecule X₂ has a body-centred cubic (bcc) structure with a cell edge of 300 pm. The density of the molecule is 6.17 g cm^–3. The number of molecules present in 200 g of X₂ is:

[Avogadro constant (N_A) = 6 × 10²³]

[JEE Main 2020, 5 Sep (Shift 1)]

An atomic substance \(A\) of molar mass \(12 g mol ^{-1}\) has a cubic crystal structure with edge length of \(300 pm\). The no. of atoms present in one unit cell of \(A\) is_______ (Nearest Integer) Given the density of \(A\) is \(3.0 g mL ^{-1}\) and \(N _{ A }=6.02 \times\) \(10^{23} mol ^{-1}\)

[JEE Main 2023, 11 Apr (Shift 1)]

A diatomic molecule X₂ has a body-centred cubic (bcc) structure with a cell edge of 300 pm. The density of the molecule is 6.17 g cm^–3. The number of molecules present in 200 g of X₂ is:

[Avogadro constant (N_A) = 6 × 10²³]

Element 'B' forms ccp structure and 'A' occupies half of the octahedral voids, while oxygen atoms occupy all the tetrahedral voids. The structure of bimetallic oxide is:

Number of crystal systems from the following where body centred unit cell can be found, is

Cubic, tetragonal, orthorhombic, hexagonal, rhombohedral, monoclinic, triclinic

[JEE Main 2023, 6 Apr (Shift 2)]

A certain element crystallises in a bcc lattice of unit cell edge length 27 Å. If the same element under the same conditions crystallises in the fcc lattice, the edge length of the unit cell (in Å) will be ______. Assume each lattice point has a single atom. Given: √3 = 1.73, √2 = 1.41

An element crystallises in a face-centred cubic (fcc) unit cell with cell edge \(a\). The distance between the centres of two nearest octahedral voids in the crystal lattice is:

A cubic solid is made up of two elements \(X\) and \(Y\). Atoms of \(X\) are present on every alternate corner and one at the center of cube. Y is at \(\frac{1}{3}\) of the total faces. The empirical formula of the compound is

[JEE Main 2023, 25 Jan (Shift 1)]

The oxide that shows magnetic property is:

[JEE Main 2021, 18 Mar (Shift 2)]

Which of the following expressions is correct in case of a \(CsCl\) unit cell (edge length 'a')?

[JEE Main 2023, 15 Apr (Shift 1)]

A sample of a metal oxide has formula \({M}_{0.83}{O}_{1.00}\). The metal M can exist in two oxidation states +2 and +3 . In the sample of \({M}_{0.83}{O}_{1.00}\), the percentage of metal ions existing in +2 oxidation state is_____ %

(Report your answer after dividing by 10) (nearest integer)