The Solid State

The Solid State

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

Answer

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
straight r space equals space fraction numerator square root of 3 over denominator 4 end fraction straight a
Now, When Na metal crystallises in bcc unit cell with unit cell edge,
a = 4.29Å 
We have the formula for radius,
i.e, straight r space equals space fraction numerator square root of 3 over denominator 4 end fraction straight x 4.29 straight Å space =1.86Å 

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