Solid State Question 303
Question: The edge length of unit cell of a metal having molecular weight 75 g/mol is $ 5\overset{{}^\circ }{\mathop{A}} $ which crystallizes in cubic lattice. If the density is 2g/cc then find the radius of metal atom. $ (N _{A}=6\times 10^{23}) $ . Give the answer in pm.
Options:
A) 217pm
B) 210pm
C) 220pm
D) 205pm
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ \rho =\frac{ZM}{N _{A}V} $
$ Z=\frac{\rho N _{A}V}{M}=\frac{2\times 6\times 10^{23}\times {{(5\times {{10}^{-8}})}^{3}}}{75} $ Z= 2, which represents bcc structure
$ \therefore ~r=\frac{\sqrt{3}}{4}a=\frac{\sqrt{3}}{4}\times 5=2.165\overset{{}^\circ }{\mathop{A}}=216.5pm $
$ \approx 217pm $
BETA
