Metallic magnesium has a hexagonal close-packed structure and a density of $2 g / cm^{3}$ . Assume magnesium atoms to be spheres of radius(r). 74% of the space of crystal is occupied by atoms.
(Given : N_A= 6 × 10²³ , (1.52)³ = 3.53, Atomic mass of Mg = 24)
Select the correct statement(s).

Question

Metallic magnesium has a hexagonal close-packed structure and a density of $2 g / cm^{3}$ . Assume magnesium atoms to be spheres of radius(r). 74% of the space of crystal is occupied by atoms.

(Given : N_A= 6 × 10²³ , (1.52)³ = 3.53, Atomic mass of Mg = 24)

Select the correct statement(s).

TestHub · Accepted Answer

Density = N A ​ V ZM ​ or, 2 = ( 6 × 1 0 23 ) × V 6 × 24 ​ or, Volume of unit cell, V = 1.2 × 1 0 − 22 cm 3 . Now, the volume occupied by the atoms = 100 74 ​ × V = 8.88 × 1 0 − 23 cm 3 Hence, the volume of each atom = 6 8.88 × 1 0 − 23 ​ = 1.48 × 1 0 − 23 cm 3 .

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