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GATE 2020 CY – Question 56

Inorganic Chemistry · Solids: Crystal systems and lattices, Miller planes, crystal packing, crystal defects, Bragg’s law, ionic crystals, structure of AX, AX2, ABX3 type compounds, spinels, band theory, metals and semiconductors, Zeolites and their applications. · 2 marks · Numerical answer

AgX has rock-salt structure, density 6477 kg/m³ and cell edge 577.5 pm. Ag atomic weight is 107.87 g/mol. Find atomic weight of X in g/mol, to 2 decimals.

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Correct answer: 79.00 to 81.00

Explanation

Rock salt has four AgX formula units per unit cell. Thus $M_{AgX}=\rho a^3N_A/4$, using consistent units. With ρ = 6.477 g/cm³ and a = 5.775×10⁻⁸ cm, M ≈ 187.81 g/mol. Subtract Ag: MX ≈ 79.94 g/mol, identifying the bromide-scale atomic weight and lying in the original 79–81 interval.

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