Sodium crystallizes in bcc arrangement with the interfacial separation between the atoms at the edge 53 pm. The density of the solid is

Question

Sodium crystallizes in bcc arrangement with the interfacial separation between the atoms at the edge 53 pm. The density of the solid is (A) 1.23 g/cc (B) 485 g/cc (C) 4.85 g/cc (D) 123 g/cc

Tardigrade Admin · Accepted Answer

Given, a-2 r=53 pm For bcc structure, 4 r=√3 a or 2 r=(√3/2) a ⇒ a-(√3/2) a=53 ∴ a=395.6 pm Density (d)=(Z M/Na a) d =(2 × 23/6.023 × 1023 ×(3.956)3 × 10-24) =1.23 g / cc .

Q. Sodium crystallizes in bcc arrangement with the interfacial separation between the atoms at the edge $53 p m$ . The density of the solid is

1.23 g/cc

485 g/cc

4.85 g/cc

123 g/cc

Given, $a - 2 r = 53 p m$
For bcc structure,
$4 r = 3 a$
or $2 r = \frac{3}{2} a$
$\Rightarrow a - \frac{3}{2} a = 53$
$∴ a = 395.6 p m$
Density $(d) = \frac{ZM}{N _{a} a}$
$d = \frac{2 \times 23}{6.023 \times 1 0 ^{23} \times ( 3.956 ) ^{3} \times 1 0 ^{- 24}}$
$= 1.23 g / cc .$

Q. Sodium crystallizes in bcc arrangement with the interfacial separation between the atoms at the edge 53pm. The density of the solid is