A metallic element crystallises in simple cubic lattice. If edge legth of the unit cell is 3 A ∘ , with density 8 g / cc , what is the number of unit cells in 100 g of the metal? ( Molar mass of metal

Question

A metallic element crystallises in simple cubic lattice. If edge legth of the unit cell is 3 A ∘ , with density 8 g / cc , what is the number of unit cells in 100 g of the metal? ( Molar mass of metal = 108 g / mol )

TestHub · Accepted Answer

( B ) a = 3 A ˚ = 3 × 1 0 − 8 cm Volume of the unit cell ( a 3 ) = ( 3 × 1 0 − 8 ) 3 cm 3 = 27 × 1 0 − 24 cm 3 Mass of unit cell = 27 × 1 0 − 24 cm 3 × 8 g cm − 3 = 216 × 1 0 − 24 g 216 × 1 0 − 24 g = 1 unit cell ∴ 108 g = ​ 216 × 1 0 − 24 108 ​ = 5 × 1 0 23 unit cells. ​

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