Solid State Question 100
Question: Select the right expression for determining packing fraction (PF) of $ NaCl $ unit cell (assume ideal), if ions along an edge diagonal are absent
Options:
A) $ PF=\frac{\frac{4}{3}\pi ( r _{+}^{3}+r _{-}^{3} )}{16\sqrt{2}r _{-}^{3}} $
B) $ PF=\frac{\frac{4}{3}\pi ( \frac{5}{3}r _{+}^{3}+4r _{-}^{3} )}{16\sqrt{2}r _{-}^{3}} $
C) $ PF=\frac{\frac{4}{3}\pi ( \frac{5}{2}r _{+}^{3}+r _{-}^{3} )}{16\sqrt{2}r _{-}^{3}} $
D) $ PF=\frac{\frac{4}{3}\pi ( \frac{7}{2}r _{+}^{3}+r _{-}^{3} )}{16\sqrt{2}r _{-}^{3}} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Effective number of states $ N{{a}^{+}}=4-( 1+2\times \frac{1}{4} )=\frac{5}{2} $
Effective number of $ C{{l}^{-}}=4\sqrt{2}a=4{{r}^{+}} $ $ PF=\frac{Volume\ of\ effective\ number\ of\ cations\ and\ anions}{Volume\ of\ unit\ cell} $
BETA
