Question

{"given":"CsBr has CsCl type structure with density 4.26 g/cm³. Atomic masses: Cs = 133 u, Br = 80 u. Avogadro's number $N_A = 6 \\times 10^{23}$ mol⁻¹. CsCl structure has simple cubic lattice with one formula unit per unit cell (Z = 1).","key_observation":"For any crystal structure, density is related to unit cell parameters by the formula: $\\rho = \\frac{Z \\times M}{N_A \\times a^3}$, where Z is the number of formula units per unit cell, M is the molar mass, and a is the edge length. In CsCl structure, both Cs⁺ and Br⁻ ions are in contact along the body diagonal, and there is exactly one formula unit per unit cell.","option_analysis":[{"label":"(A)","text":"5.503 Å","verdict":"incorrect","explanation":"This value is too large. Using the density formula with this edge length would give a density much lower than the given 4.26 g/cm³, indicating this cannot be the correct answer."},{"label":"(B)","text":"4.368 Å","verdict":"correct","explanation":"Using density formula: $a^3 = \\frac{Z \\times M}{\\rho \\times N_A} = \\frac{1 \\times 213}{4.26 \\times 6 \\times 10^{23}} = 8.332 \\times 10^{-23}$ cm³. Taking cube root gives a = 4.368 × 10⁻⁸ cm = 4.368 Å."},{"label":"(C)","text":"3.225 Å","verdict":"incorrect","explanation":"This edge length is too small. Substituting this value back into the density equation would yield a density significantly higher than 4.26 g/cm³, making it inconsistent with the given data."},{"label":"(D)","text":"2.856 Å","verdict":"incorrect","explanation":"This is the smallest value and would result in an unrealistically high calculated density when used in the density formula, much greater than the given 4.26 g/cm³."}],"answer":"(B)","formula_steps":[]}