Question

Sodium metal crystallises in bcc lattice with the cell adge, $a$ equal to $42.29\mathring{A}$. What is the radius (in $\mathring{A}$) of sodium atom?

• A. $1.86$
• B. $1.90$
• C. $18.3$
• D. $1.12$

Answer 1

Answer: (C)

$18.3$

The relationship between the radius r and the edge length a is as given below:
$a=\frac{4r}{\sqrt{3}}$
The above expression can be rearranged as $r=\frac{\sqrt{3}a}{4}$
Substituting values in the above expression, we get,
$r=\frac{1.732\times 42.029}{4}=18.31\mathring{A}$
Hence, the radius of sodium atom is $18.3\mathring{A}$.