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Question

Chemistry Question on The solid state

Vacant Space in a body centered cubic lattice unit cell is about

A

23%

B

32%

C

46%

D

10%

Answer

32%

Explanation

Solution

"To determine the vacant space in a BCC lattice unit cell, we need to consider the arrangement of atoms or ions and the spaces left between them.
In a BCC lattice, each lattice point is occupied by an atom or ion, and there is a vacant space in the center of the unit cell. This vacant space is often referred to as an octahedral void.
The volume of the octahedral void is equal to the volume of one atom or ion. In a BCC lattice, the volume occupied by the atoms or ions is equal to the volume of the eight atoms or ions at the corners plus the volume of the one atom or ion at the center.
Therefore, the vacant space in a BCC lattice unit cell is given by: Vacant space = (Volume of octahedral void) / (Total volume of the unit cell) * 100
Since the volume of the octahedral void is equal to the volume of one atom or ion, and the total volume of the unit cell is the sum of the volumes of the atoms or ions at the corners and the center, we can calculate the vacant space.
The vacant space in a BCC lattice unit cell is approximately 32% (option B)."