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Question

The density of chromium metal is 7.2 g cm3. If the unit cell is cubic with an edge length of 289 pm, determine the type of unit cell (simple, body centred or face centred). [Atomic mass of Cr=52 amu, NA=6.02×1023 mol1]

A
SC
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B
BCC
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C
FCC
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D
HCP
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Solution

The correct option is B BCC
The expression for density is as follows:
Density =d=n×MMa3×NA
Given: d =7.2 g cm3
a = 289 pm =289×1010cm
Molecular weight of Cr = 52 g mol1
n=d×a3×NAMM
n=7.2×(289×1010)3×6.02×102352
n = 2

Since there are 2 Cr atoms in a unit cell, Cr crystallizes in a bcc unit cell.

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