Question

An element having BCC crystal structure has atomic mass $50$ amu and the density is $6.81$ g cm${}^{-3}$. Calculate the edge length (in pm) of unit cell.

• A. $380$
• B. $290$
• C. $195$
• D. $145$

Answer 1

Answer: (B)

$290$

The expression for calculating edge length is as follows:

$a^3=\frac{Z\times M}{d\times N_A}=\frac{2\times 50}{6.81\times 6.02\times {10}^{23}}$ $=2.44\times {10}^{-23}$ cm${}^3$

$\text{Edge length,}a={(2.44\times {10}^{-23})}^{\frac{1}{3}}=2.9\times {10}^{-8}cm=290pm$