Question
Sodium metal crystallises in a body centred cubic lattice with a unit cell edge of 4.29 Å The radius of sodium atom is approximate:
-
1.86 Å
-
3.22Å
-
5.72 Å
-
0.93 Å
Solution
A.
1.86 Å
According to the figure
(AC)2 = (AB)2 + (BC)2
(AC)2 = a2 + a2 = 2a2
(AD)2 = (AC)2+ (DC)2
(4r)2 = 2a2 + a2
16r2 = 3a2
Now, When Na metal crystallises in bcc unit cell with unit cell edge,
a = 4.29Å
We have the formula for radius,
i.e,
=1.86Å
Now, When Na metal crystallises in bcc unit cell with unit cell edge,
a = 4.29Å
We have the formula for radius,
i.e,
=1.86Å 
