Q.

An element crystallises as face centred cubic lattice with density as 5.20 g / cm3 and edge length of the side of unit cell as 300 pm. The  mass of the element which contains 3.0×1024 cannot be equal to

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a

55g

b

105g

c

205g

d

275g

answer is A.

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Detailed Solution

Z = 4 in fcc lattice M = ?. d = 5.20 g / cm3a = 300, pm = 300 × 10-12. m = 3 × 10-10. m = 3 × 10-6 cm3∴            a3=27×10−24  cm3N0=6.02×1023∴          M=dN0a3Z=5.20 g/cm3×6.02×1023 mol−1×27×10−24 cm34= 21.13 g mol-1Thus, 6.02×1023 atmos have = 21.13 g∴    3.01×1024  atoms have = 21.136.02×1023×3.01×1024 g=105.65 g
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