First slide

Crystal lattices and unit cells

Question

A compound M_pX_q has cubic close packing (ccp) arrangement of X. Its unit cell structure shown below. The empirical formula of the compound is:

Moderate

A

MX
B

MX₂
C

M₂X
D

M₅X₁₄

Solution

8 X atoms present at the corners.
Atoms contribute to 1 unit cell $= \frac{1}{8} \times 8 = 1$
6X atoms present at the face centres.
$Atoms contribute to 1 unit cell = 6 \times \frac{1}{2} = 3$
Total X atoms =3 + 1=4
4 M atoms present at edge centres.
$Atoms present in 1 unit cell = 4 \times \frac{1}{4} = 1$
1M atom present at body centre and it contribute completely to 1 unit cell
Thus, total M atoms in one unit cell = 1+1=2
Ratio is M:X::2:4::1:2
Thus, empirical formula is MX₂.

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