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An ionic solid MX crystallizes in a face-centered cubic lattice where anions X ^- occupy the lattice points and cations M ^+ occupy all the octahedral voids. If the edge length of the unit cell is 514 pm and the ionic radius of the anion X ^- is 181 pm , the ionic radius of the cation M ^+ is _____ pm .

Correct answer

76

Step-by-step solution

In a face-centered cubic lattice where anions form the lattice and cations occupy all octahedral voids, the structure is of the rock-salt ( NaCl ) type. In this structure, the cations and anions touch each other along the edge of the unit cell. The relationship between the edge length ( a ) and the ionic radii ( r_+ and r_- ) is given by: a = 2(r_+ + r_-) Given: a = 514 pm r_- = 181 pm Substituting the given values: 514 = 2(r_+ + 181) 257 = r_+ + 181 r_+ = 257 - 181 = 76 pm Answer: 76

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