An ionic compound $A_xB_y$ crystallizes in fcc type crystal structure with B ions at the centre of each face and A ion occupying corners of the cube. The correct formula of $A_xB_y$ is (a) AB (b) $AB_3$ (c) $A_3B$ (d) $A_8B_6$

An ionic compound AₓBy crystallizes in fcc type crystal structure with B ions at the centre of each face and A

Choose the Best Answer · Q2

A_xB_y

(a) AB

(b)

AB_3

(c)

A_3B

(d)

A_8B_6

Tamil Nadu DgeTextbookSubjectiveImportance★★★★★

4% · 3/70 Questions

✓ Free question

Concept understanding — Unit Cell Types — Primitive, Non-Primitive and the Seven Crystal Systems

There are exactly seven primitive crystal systems, distinguished by how their three edge lengths and three angles relate: cubic (a=b=c, all angles 90 deg), tetragonal (a=b not-eq c, all 90 deg), orthorhombic (a not-eq b not-eq c, all 90 deg), hexagonal (a=b not-eq c, alpha=beta=90 deg, gamma=120 deg), rhombohedral (a=b=c, all angles equal but not 90 deg), monoclinic (a not-eq b not-eq c, alpha=gamma=90 deg, beta not-eq 90 deg), and triclinic (a not-eq b not-eq c, no angle equal to 90 deg or to another). Once possible centrings (body-centred, face-centred, base-centred) of these seven are also counted, Bravais showed only 14 distinct lattices are geometrically possible -- the 14 Bravais lattices (Table 6.2): 3 cubic + 2 tetragonal + 1 hexagonal + 4 orthorhombic + 2 monoclinic + 1 trigonal + 1 triclinic = 14.

For the three cubic unit cells, the number of atoms belonging to one cell is found by weighting each shared lattice position: a corner atom (shared by 8 cells) contributes 1/8; a face-centred atom (shared by 2 cells) contributes 1/2; a body-centred atom (unshared) contributes a full 1.

Simple cubic (SC): atoms at 8 corners only. Atoms/cell = 8x(1/8) = 1. Coordination number 6 (touch along edges only, a = 2r).
Body-centred cubic (BCC): 8 corners + 1 body centre. Atoms/cell = 8x(1/8) + 1 = 2. Coordination number 8 (corners don't touch each other, all touch the body-centre atom; body diagonal root-3*a = 4r).
Face-centred cubic (FCC): 8 corners + 6 face centres. Atoms/cell = 8x(1/8) + 6x(1/2) = 4. Corner atoms touch face atoms, not each other; face diagonal root-2*a = 4r.

This same corner/face/body-sharing logic extends beyond simple 3-D atom counts -- e.g. to a 2D-pattern unit cell, or to an ionic AxBy compound where different ions sit at different shared positions (corners vs face centres vs body centre), letting the compound's simplest formula be read directly off the unit cell diagram.

Step 1. A ions occupy the 8 corners of the cube. Each corner ion is shared by 8 unit cells, so A contributes $8 \times \tfrac{1}{8} = 1$ to this cell.

Step 2. B ions occupy the centre of each of the 6 faces. Each face ion is shared by 2 unit cells, so B contributes $6 \times \tfrac{1}{2} = 3$ to this cell.

Step 3. So one unit cell contains 1 A and 3 B, giving the ratio A:B = 1:3, i.e. the simplest formula is $AB_3$ .

✓Final answer

AB_3

Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2024Set ANNUAL1 markMCQ
$a \ne b \ne c$
(a) Assertion is true but Reason is false.
(b) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
(c) Both Assertion and Reason are false.
(d) Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion.
›Reveal solutionSolution

Monoclinic sulphur is a genuine example of the monoclinic crystal system, and the reason correctly states that system's defining unequal edge lengths and single non-90° angle — both true, and the reason correctly explains the assertion.

Seven crystal systems are classified by their unit-cell edge lengths ( $a,b,c$ ) and inter-axial angles ( $\alpha,\beta,\gamma$ ). The monoclinic system is defined by $a\ne b\ne c$ (three unequal edges) and $\alpha=\gamma=90°$ , $\beta\ne90°$ (two right angles and one oblique angle) — exactly as the reason states, so the reason is a true and accurate statement of the general monoclinic system's parameters. Monoclinic sulphur (one of the allotropic crystalline forms of sulphur, stable above 96°C, alongside rhombic sulphur) is a standard textbook example of a substance crystallising in this monoclinic system, so the assertion is also true. Since the reason directly and correctly defines the very crystal system the assertion places monoclinic sulphur in, it is the correct explanation of the assertion.

✓Final answer
$a\ne b\ne c$

←Previous question · evaluationQ1 — Graphite and diamond are (a) Covalent and molecular crystals (b) ionic…→Next question · evaluationQ3 — The ratio of close packed atoms to tetrahedral hole in cubic packing i…

Q.An ionic compound AxByA_xB_yAx​By​ crystallizes in fcc type crystal structure with B ions at the centre of each face and A ion occupying corners of the cube. The correct formula of AxByA_xB_yAx​By​ is

🎓Unlock everything free for 14 days

Q.An ionic compound $A_xB_y$ crystallizes in fcc type crystal structure with B ions at the centre of each face and A ion occupying corners of the cube. The correct formula of $A_xB_y$ is

Unlock everything free for 14 days