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Question:

The arrangement of X⁻ ions around A⁺ ion in solid AX is given in the figure (not drawn to scale). If the radius of X⁻ is 250 pm, the radius (in pm) of A⁺ will be:

125

57

104

183

Solution:

According to the given figure, A⁺ is present in the octahedral void of X⁻. The limiting radius in an octahedral void is related to the radius of the sphere as:

Radius of cation (A⁺) / Radius of anion (X⁻) = 0.414

Given that the radius of X⁻ is 250 pm, we can calculate the radius of A⁺:

Radius of A⁺ = 0.414 × Radius of X⁻
Radius of A⁺ = 0.414 × 250 pm
Radius of A⁺ = 103.5 pm

The closest option to 103.5 pm is 104 pm.