Question

Sodium metal crystallizes as a body-centred cubic lattice with the cell edge $4.29\mathring{A}$. What is the radius of the sodium atom?

• A. 1.857 $\times$ ${10}^{-8}$ cm
• B. 2.371 $\times$ ${10}^{-7}$ cm
• C. 3.817 $\times$ ${10}^{-8}$ cm
• D. 9.312 $\times$ ${10}^{-7}$ cm

Answer 1

The correct option is A 1.857 $\times$ ${10}^{-8}$ cm

Let us consider for body center unit cell.

$4r=a\sqrt{3}$

Therefore,

Radius of $Na=\frac{\sqrt{3}}{4}a$

$=\left(\frac{\sqrt{3}}{4}\right)\left(4.29\times {10}^{-8}\right)$

$=1.86\stackrel{\circ }{A}\approx 1.86\times {10}^{-8}cm$