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Calculate the critical radius ratio of an ionic crystal in ligancy 6 . what is the maximum size of cation in ligancy 6 configuration when size of anion is 2.02Angstrom
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OCTAHEDRAL CONFIGURATION:

The octahedral configuration of neighbouring anions is found in NaCl structure. Here four anions A, B ,C and D are arranged at the corners of a square with the cation O at the centre of the square. Two more anions are situated in front and at the back of the cation. The centres of all six anions form an octahedron.

Here in ∆ BOC , < BOC = 90°, BC = 2rA , OB =rC+rA and <bco =45°,<="" p="">

Hence, BO/BC=cos45°

Or, (rC+rA)/(2rA)=1/(2)

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The critical radius ratio here is,

NUMERICAL:

Given data :- rA(max)=2.02A° , ligancy = 6.

Formula :- for ligancy 6 ,(rC/rA) = 0.732.

Calculations :- rC=rA×0.732=2.02×0.732=1.478A°

Answer :- rC=1.478A°

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