GATE ME 2026 Set 1 — Question 62
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Engineering Materials → Structure & Properties → Crystal Structures & Imperfections
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Question
A metal has FCC crystal structure with 2.71 g/cm of density and 26.98 g/mol of atomic weight. The Avogadro’s number is . The atomic radius of the metal is ________ nm (rounded off to 2 decimal places).
Correct answer
0.12 to 0.16
Solution
Given data:
Crystal structure: FCC (Face-Centered Cubic), so number of atoms per unit cell () = 4
Density () = 2.71 g/cm
Atomic weight () = 26.98 g/mol
Avogadro's number () = molThe formula for density is:where is the lattice parameter.Rearranging for :For an FCC structure, the relationship between atomic radius () and lattice parameter () is:Rounding to 2 decimal places, the atomic radius is 0.14 nm.
Crystal structure: FCC (Face-Centered Cubic), so number of atoms per unit cell () = 4
Density () = 2.71 g/cm
Atomic weight () = 26.98 g/mol
Avogadro's number () = molThe formula for density is:where is the lattice parameter.Rearranging for :For an FCC structure, the relationship between atomic radius () and lattice parameter () is:Rounding to 2 decimal places, the atomic radius is 0.14 nm.
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