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Question

CsCl crystals are formed by bcc crystal lattice where Cl occupies the corners and Cs+ occupies the centre of the cube.

The density of crystalline CsCl is 4 g/cc. The effective volume occupied by a single CsCl ion pair in the crystal is
[Molar mass of CsCl=168 g mol1

A
7×1023cc
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B
14×1022cc
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C
5×1023cc
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D
12×1023cc
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Solution

The correct option is A 7×1023cc
In bcc, the ions are present in the corners and body centre of the cube.
Number of Clper unit cell =18×8=1
Number of Cs+per unit cell =1
Hence, an unit cell of CsCl comprise of one ion pair of CsCl
Thus, volume of the unit cell gives the effective volume occupied by a single CsCl ion pair.

Density of unit cell, ρ=ZMVNA
where,
Z is the number of atoms in unit cell
M is the molar mass
NA is the avagadro number.
V is the volume of unit cell.
Since, one ion pair of CsCl is present in the unit cell, the value of Z is 1

d=1×1686.023×1023×a3=4 g/cc
a3=1×1686.023×4×1023=7×1023cc.

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