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In an ionic crystal, anions Q ^- form a cubic close-packed (ccp) lattice and cations P ^+ occupy all the octahedral voids. The ionic radii of P ^+ and Q ^- are 120 pm and 200 pm respectively. If the shortest distance between two P ^+ ions in the crystal is x 2 pm , the value of x is _____.

Correct answer

320

Step-by-step solution

The anions Q ^- form a ccp lattice and cations P ^+ occupy all octahedral voids. This corresponds to a rock-salt type structure. The edge length ( a ) of the unit cell is determined by the contact of ions along the edge: a = 2(r_+ + r_-) a = 2(120 + 200) = 2(320) = 640 pm The cations P ^+ are located at the octahedral voids, which are present at the center of each edge and at the body center of the unit cell. The shortest distance between two octahedral voids (for example, between an edge center and the body center

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