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If the unit cell of a mineral with formula $M g A l 2 O 4$ has cubic close packed (ccp) array of oxygen atoms with m fraction of octahedral holes occupied by aluminium ions and n fraction of tetrahedral holes occupied by magnesium ions, m and n, respectively the value of $1 n − 1 m$ is ________

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answer is 6.

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Detailed Solution

O 2 − − 4 O h = 4

A l 3 + − 2 t d = 8

M g 2 + − 12 o h

voids & 1td void

∴ m = 24 = 12

n = 18

1 n − 1 m = 8 − 2 = 6

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