Question

{"given":"Oxide ions are arranged in CCP (cubic close packing) arrangement. Cations A occupy one-sixth of the tetrahedral voids. Cations B occupy one-third of the octahedral voids. We need to determine the formula of the compound.","key_observation":"In CCP arrangement, if there are N oxide ions, there are N tetrahedral voids and N/2 octahedral voids. The number of each type of cation depends on the fraction of voids occupied. The formula is determined by finding the simplest whole number ratio of A:B:O.","option_analysis":[{"label":"(A)","text":"$AB_2O_4$","verdict":"incorrect","explanation":"This formula suggests A:B:O ratio of 1:2:4, which doesn't match our calculated ratio of 1:1:3 from the void occupation data."},{"label":"(B)","text":"$ABO_3$","verdict":"correct","explanation":"This gives A:B:O ratio of 1:1:3. From our calculation: A ions = N/6, B ions = N/6, O ions = N, giving ratio (N/6):(N/6):N = 1:1:6. Dividing by 2 gives 1:1:3, matching $ABO_3$."},{"label":"(C)","text":"$ABO_2$","verdict":"incorrect","explanation":"This formula suggests A:B:O ratio of 1:1:2, which doesn't match our calculated ratio of 1:1:3 from the void occupation analysis."},{"label":"(D)","text":"$ABO_4$","verdict":"incorrect","explanation":"This formula suggests A:B:O ratio of 1:1:4, which doesn't match our calculated ratio of 1:1:3 from the void occupation data."}],"answer":"(B)","formula_steps":[]}