The Solid State

The Solid State

Question

An element ‘X’ (At. mass = 40 g mol–1) having f.c.c. the structure has a unit cell edge length of 400 pm. Calculate the density of ‘X’ and the number of unit cells in 4 g of ‘X’. (NA = 6.022 × 1023 mol–1 )

Answer

We know,

d = Z x MNA x a3For FCC Z is 4d = 4 x 406.022 x 1023 x (400 x 10-10)3 = 4.1514 gm cm-3Volume  of 4 gm X is 44.1514 cm3 = 0.96 cm3Volume of 1 unit cell is = (400 x 10-10)3 cm3 = 64 x 10-24 cm3Number  of unit cell  = 0.9664 x 10-24 = 1.5  x 1022

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