Question

An element has a body centered cubic structure with a unit cell edge length of $100\, pm$. Atomic mass of an element is $24\, g\, mol ^{-1}$. What is the density of the element? $\left( N _{A}=6 \times 10^{23}\, mol ^{1}\right)$

• A. $2.50\, g\, cm ^{-3}$
• B. $1.80\, g\, cm ^{-3}$
• C. $3.60\, g\, cm ^{-3}$
• D. $1.25\, g\, cm ^{-3}$

Answer 1

Answer: (D)

Given,

Body centered cubic st. i.e. $Z=2$

edge length $(a)=400\, pm$.

$=400 \times 10^{-10}$

$M ($ atomic mass $)=24\, g\, mol ^{-1}$

$N_{A}=6 \times 10^{23}\, mol ^{-1}$

$\because$ Density $(d)=\frac{Z \times M}{a^{3} \times N_{A}}$

$d=\frac{2 \times 24}{\left(400 \times 10^{-10}\right)^{3} \times 6 \times 10^{23}}$

$d=125\, g\, cm ^{-3}$