Q. The radii of $Na^{+}$and $Cl^{-}$ ions are 95 pm and 181 pm respectively. The edge length of $NaCl$ unit cell is

A) 276 pm
B) 138 pm
C) 552 pm
D) 415 pm
Explanation

(c)
$NaCl\$ has fcc structure.
In fcc lattice
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ r^{+} + r^{-} = \frac{a}{2}$
Where, $a =$ edge length
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ r^{+} = 95\ pm,\ r^{-} = 181\ pm\$
Edge length $= 2r^{+} + 2r^{-}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = (2 \times 95 + 2 \times 181)\ pm$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 190 + 362 = 552\ pm$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.