37. Sodium has body centred packing. Distance between two nearest atoms is 3.7Â. The lattice parameter is ?

37. Sodium has body centred packing. Distance between two nearest atoms is 3.7Â. The lattice parameter is ?

(a) 4.3 A

(b) 3.0 A

(c) 8.6 A

(d) 6.8 A

Answer :  (a) 4.3 A

\(  x^2 = \left( \frac{A}{2} \right)^2 + \left( \frac{A}{2} \right)^2 + \left( \frac{A}{2} \right)^2  \)

\( = \frac{3A^2}{4} \)

\( x = A\sqrt{\frac{3}{2}} \)

\( \sqrt{\frac{3}{2}}\,A = 3.7\hat{A} \)

\( A = \frac{3.7 \times 2}{1.7}\hat{A} \)

\( = 4.3\hat{A} \)