Calculate the molar mass of an element if it forms fcc unit cell structure [mass of unit cell =1.8 10⁻²² ~g , ~N _ A =6.022 10²³ ~mol ⁻¹ ]

Step-by-step solution

Molar mass calculation for FCC unit cell The face-centered cubic structure has Z = 4 atoms per unit cell, calculated as 8 1 8 + 6 1 2 = 4 atoms. Given the unit cell mass as 1.8 10⁻²² g, the mass per atom is m = 1.8 10⁻²² 4 = 4.5 10⁻²³ g. Using Avogadro's number N_A = 6.022 10²³ mol⁻¹, the molar mass becomes: M = m N_A = (4.5 10⁻²³) (6.022 10²³) = 27.099 g mol⁻¹ The calculated molar mass of 27.1 g mol⁻¹ corresponds to option A: 27.0 g mol⁻¹. Final answer: A