Question

The edge length of unit cell of a metal having molar mass $75$ g mol${}^{-1}$ is $5\mathring{A}$ which crystallizes in body centered cubic lattice. If density is $2$ g cm${}^{-3}$, calculate the radius (in pm) of metal atom.

• A. $216$
• B. $214$
• C. $100$
• D. $2.14$

Answer 1

Answer: (A)

$216$

The expression for density is as follows:

$\text{Density}=\frac{n\times \text{Molar mass}}{V\times N_a}$
$2=\frac{2\times 75}{a^3\times 6.023\times {10}^{23}}$ ($n=2$ for bcc)
$\therefore a=5\times {10}^{-8}$ cm${}^3$
$\because r=\frac{\sqrt{3}}{4}\times a=\frac{\sqrt{3}}{4}\times 5\times {10}^{-8}$ $=2.16\times {10}^{-8}$ cm $=216$ pm