A crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of 400 pm, if the density of the substance in the crystal is 8 g c m - 3 , then the number of atoms present

Question

A crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of 400 pm, if the density of the substance in the crystal is 8 g c m - 3 , then the number of atoms present in 256 g of the crystal is N × 1 0 24 . The value of N is

TestHub · Accepted Answer

d = Z × M a 3 × N A M = ( 400 ) 3 × 1 0 - 30 × 8 × N A 4 On solving M = 64 × 2 × 1 0 - 24 N A g Now, ( 64 × 2 × 1 0 - 24 N A ) g contains N A atoms As 256 g = N A 64 × 2 × 1 0 - 24 N A × 256 = 2 × 1 0 24

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