Question:

The density of a metal which crystallises in $bcc$ lattice with unit cell edge length $300\,pm$ and molar mass $50 \,g \,mol^{-1}$ will be

Updated On: Jul 7, 2022

$10\, g\,cm^{-3}$
$14.2\, g\,cm^{-3}$
$6.15\, g\,cm^{-3}$
$9.32\, g\,cm^{-3}$

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The Correct Option is C

Solution and Explanation

$d=\frac{Z\times M}{a^{3}\times N_{A}}$ For $bcc$ structure, $Z = 2$ $d=\frac{2\times50}{6.023\times10^{23}\times\left(300\times10^{-10}\right)^{3}}$ $=6.15\,g\,cm^{-3}$

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Notes on Unit Cells

Unit Cell Chemistry

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.
1. 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.
2. Face Centered Unit Cell: Such a unit cell contains one constituent particle present at the centre of each face, as well as its corners.
3. 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.