For the ionic compound A_3 ~B , which of the following statements are correct, if radii of A^ - and B^ 3+ ion are respectively 5 x and 2 x and the lattice points have hcp arrangement?

Correct answer: C. The coordination number of B^ 3+ is 4 Radius ratio ( ^ + ^ - )= 2 x 5 x =0.4 , coordination number of B^ 3+ 4 Formula of the compound is A_3 B , i.e., (1)/(6) th of tetrahedral sites are occupied by B^ 3+ and so vacant tetrahedral sites are (5)/(6) th.

JEE Advanced

Exam: JEE Advanced
Subject: Chemistry
Chapter: Solid State

JEE Advanced · Chemistry · Solid State

For the ionic compound A_3 ~B , which of the following statements...

For the ionic compound

\mathrm{A}_3 \mathrm{~B}

, which of the following statements are correct, if radii of

\mathrm{A}^{-}

and

\mathrm{B}^{3+}

ion are respectively

5 x

and

2 x

and the lattice points have hcp arrangement?

Options

A $\frac{5}{6}$ th of tetrahedral voids are vacant
B $\frac{1}{3}$ rd of total voids are vacant in compound
CThe coordination number of $\mathrm{B}^{3+}$ is 4
DThe coordination number of $\mathrm{A}^{-}$ is 8

Correct answer

C. The coordination number of $\mathrm{B}^{3+}$ is 4

Step-by-step solution

Radius ratio \left(\frac{\mathrmr^{+}}{\mathrmr^{-}}\right)=\frac{2 \mathrm{x}}{5 \mathrm{x}}=0.4

, coordination number of

\mathrm{B}^{3+} \Rightarrow 4

Formula of the compound is

A_3 B

, i.e.,

\frac{1}{6}

th of tetrahedral sites are occupied by

\mathrm{B}^{3+}

and so vacant tetrahedral sites are

\frac{5}{6}

th.

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