Paragraph: In a cubic unit cell, atoms (A) are present at all...

Paragraph: In a cubic unit cell, atoms (A) are present at all corners, (B) are present at alternate face centre and all edge centres. Atoms (C) are present at face centres left from (B) and one at each body diagonal at distance of

1 / 4^{\text {th }}

of body diagonal from corner.Question: An axis is passed from the given unit cell connecting opposite face centres and all atoms touching the axis are removed. The possible formula of compound left is

Options

A $\mathrm{AB}_3 \mathrm{C}_6$ or $\mathrm{AB}_4 \mathrm{C}_5$
B $\mathrm{A}_3 \mathrm{~B}_6 \mathrm{C}_7$ or $\mathrm{A}_3 \mathrm{~B}_6 \mathrm{C}_5$
C $\mathrm{A}_4 \mathrm{~B}_5 \mathrm{C}_8$ or $\mathrm{A}_4 \mathrm{~B}_5 \mathrm{C}_7$
D $\mathrm{AB}_2 \mathrm{C}$ or $\mathrm{ABC}_2$

Correct answer

A. $\mathrm{AB}_3 \mathrm{C}_6$ or $\mathrm{AB}_4 \mathrm{C}_5$

Step-by-step solution

If axis passes through face centre where

B

lies, then Number of B atoms

=4-

\left(\frac{1}{2} \times 2\right)=3

Formula

=\mathrm{AB}_3 \mathrm{C}_6

If axis passes through face centres where C lies, then Number of

atoms

=6-\frac{1}{2} \times 2=5\therefore

Formula

=\mathrm{AB}_4 \mathrm{C}_5

Practice Solid State on Quantrex Academy →

More from Solid State

The density (in g cm^ -3 ) of the metal which forms a cubic close packed (ccp) lattice… JEE Advanced 2025 Atoms of metals x, y and z form face-centred cubic (fcc) unit cell of edge length L _ x… JEE Advanced 2023 Which of the following expressions is correct in case of a CsCl unit cell (edge length… JEE Main 2023 Sodium metal crystallises in a body centred cubic lattice with unit cell edge length of… JEE Main 2023 An atomic substance A of molar mass 12g mol ^ – 1 has a cubic crystal structure with edge… JEE Main 2023 The correct relationships between unit cell edge length ‘ a ’ and radius of… JEE Main 2023 Number of crystal systems from the following where body centred unit cell can be found… JEE Main 2023 A compound is formed by two elements X and Y . The element Y forms cubic close packed… JEE Main 2023 Full Solid State list All Most Important Selected Qs for JEE Advanced PYQs