Question:
The edge length of a $fcc$ ionic crystal is 508 pm. If the radius of cation is 110 pm, the radius of anion will be
The edge length of a $fcc$ ionic crystal is 508 pm. If the radius of cation is 110 pm, the radius of anion will be
Updated On: Jun 7, 2022
- 398 pm
- 288 pm
- 144 pm
- 618 pm
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The Correct Option is C
Solution and Explanation
For ionic compounds,
Edge length $(a) = 2(r_+ + r_-)$
$508 = 2(110 + r_-)$
$508 = 220 + 2r_-$
$2r- = 508 - 220 = { 288\, pm}$
$r_- = {144 \,pm}$
Edge length $(a) = 2(r_+ + r_-)$
$508 = 2(110 + r_-)$
$508 = 220 + 2r_-$
$2r- = 508 - 220 = { 288\, pm}$
$r_- = {144 \,pm}$
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Concepts Used:
Unit Cells
The smallest portion of a crystal lattice which repeats in different directions to form the entire lattice is known as Unit cell.
The characteristics of a unit cell are:
- The dimensions are measured along the three edges, a, b and c. These edges can form different angles, they may be mutually perpendicular or may not.
- The angles held by the edges are α (between b and c) β (between a and c) and γ (between a and b).
Therefore, a unit cell is characterised by six parameters such as a, b, c and α, β, γ.
Types of Unit Cell:
Numerous unit cells together make a crystal lattice. Constituent particles like atoms, molecules are also present. Each lattice point is occupied by one such particle.
- Primitive Unit Cells: In a primitive unit cell constituent particles are present only on the corner positions of a unit cell.
- Centred Unit Cells: A centred unit cell contains one or more constituent particles which are present at positions besides the corners.
- Body-Centered Unit Cell: Such a unit cell contains one constituent particle (atom, molecule or ion) at its body-centre as well as its every corners.
- Face Centered Unit Cell: Such a unit cell contains one constituent particle present at the centre of each face, as well as its corners.
- End-Centred Unit Cells: In such a unit cell, one constituent particle is present at the centre of any two opposite faces, as well as its corners.