Solid State Question 34
Question: A metal has fcc lattice. The edge length of the unit cell is 404 pm. The density of the metal is $ 2.72gc{{m}^{-3}}. $ The molar mass of the metal is: ( $ N _{A} $ Avogadro’s constant $ =6.02\times 10^{23}mo{{l}^{-1}} $ )
Options:
A) $ 30g mo{{l}^{-1}} $
B) $ 27g mo{{l}^{-1}} $
C) $ 20g mo{{l}^{-1}} $
D) $ 40g mo{{l}^{-1}} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Density is given by $ d=\frac{Z\times M}{N _{A}a^{3}}; $ where Z = number of formula units present in unit cell, which is 4 for fcc a = edge length of unit cell. M= Molecular mass $ 2.72=\frac{4\times M}{6.02\times 10^{23}\times {{( 404\times {{10}^{-10}} )}^{3}}} $
$ (\therefore 1 pm={{10}^{-10}}cm) $
$ M=\frac{2.72\times 6.02\times {{(404)}^{3}}}{4\times 10^{7}} $
$ =26.99=27gmmol{{e}^{-1}} $
BETA
