Question

An element (atomic mass $100g/mol$) having $BCC$ structure has unit cell edge $400pm$. The density of element is:

(No. of atoms in $BCC,Z=2$)

• A. $2.144g/c{m}^3$
• B. $7.289g/c{m}^3$
• C. $5.188g/c{m}^3$
• D. $10.376g/c{m}^3$

Answer 1

Answer: (C)

$5.188g/c{m}^3$

Mass of two atoms $=\frac{100}{6.02\times {10}^{23}}\times 2g$

$=\frac{2}{6.02}\times \frac{{10}^{-21}}{{10}^3}kg$

volume of cell $=(4\times {10}^{-10}{)}^3=64\times {10}^{-30}{m}^3$

$Density=\frac{mass}{volume}=\frac{2\times {10}^{24}}{6\times {10}^{-30}\times 6.02}$

$Density=\frac{2}{6.02\times 64}\times {10}^{6}kg/m^3$

$=\frac{2\times {10}^6\times {10}^3}{6.02\times 64\times {10}^6}gm/cc$

$=\frac{2}{6.02\times 64}\times {10}^{3}gm/cc=5.188/gm/cc$