Question

{"given":"An ionic solid has HCP (hexagonal close packing) arrangement of Q²⁻ ions. P^x+ ions occupy half of the tetrahedral voids in this structure. We need to find the value of x for charge neutrality.","key_observation":"In HCP arrangement, there are 2 tetrahedral voids per atom in the close-packed structure. If P^x+ ions occupy half of these voids, then the number of P^x+ ions equals the number of Q²⁻ ions. For the ionic compound to be electrically neutral, the total positive charge must equal the total negative charge.","option_analysis":[{"label":"(A)","text":"1","verdict":"incorrect","explanation":"If x = 1, we have equal numbers of P⁺ and Q²⁻ ions. Total positive charge = N × (+1) = +N, total negative charge = N × (-2) = -2N. Net charge = +N - 2N = -N ≠ 0, so not neutral."},{"label":"(B)","text":"2","verdict":"correct","explanation":"If x = 2, we have equal numbers of P²⁺ and Q²⁻ ions. Total positive charge = N × (+2) = +2N, total negative charge = N × (-2) = -2N. Net charge = +2N - 2N = 0, achieving charge neutrality."},{"label":"(C)","text":"4","verdict":"incorrect","explanation":"If x = 4, we have equal numbers of P⁴⁺ and Q²⁻ ions. Total positive charge = N × (+4) = +4N, total negative charge = N × (-2) = -2N. Net charge = +4N - 2N = +2N ≠ 0, so not neutral."},{"label":"(D)","text":"1/2","verdict":"incorrect","explanation":"If x = 1/2, we have equal numbers of P^{1/2+} and Q²⁻ ions. Total positive charge = N × (+1/2) = +N/2, total negative charge = N × (-2) = -2N. Net charge = +N/2 - 2N = -3N/2 ≠ 0, so not neutral."}],"answer":"(B)","formula_steps":[]}