Question

Tungsten has a body centred cubic lattice and each lattice point is occupied by one atom. If density of tungsten is $19.30$ gcm${}^{-3}$ and atomic mass is $183.9$ amu, the radius of metallic tungsten (in $\mathring{A}$) will be:

• A. $1.37$
• B. $1.17$
• C. $1.76$
• D. $1.91$

Answer 1

The correct option is A $1.37$

density $=\frac{zM}{N_a\times (a\times {10}^{-10}{)}^3}$

$19.3=\frac{2\times 183.9}{6\times {10}^{23}\times (a{)}^3}$

$a^3=3.17\times {10}^{-23}$

$a=3.17\times {10}^{-8}$

In body centered cubic,

$4r=a\sqrt{3}$

$r=\frac{a\sqrt{3}}{4}$

$r=1.37\mathring{A}$

Hence, the correct option is $A$