Question

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

• A. $2.50gc{m}^{-3}$
• B. $1.80gc{m}^{-3}$
• C. $3.60gc{m}^{-3}$
• D. $1.25gc{m}^{-3}$

Answer 1

Answer: (D)

Given,

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

edge length $(a)=400pm$.

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

$M($ atomic mass $)=24gmo{l}^{-1}$

$N_A=6\times 10^{23}mo{l}^{-1}$

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

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

$d=125gc{m}^{-3}$