Question
A compound crystallizes in bcc structure. What is unit cell edge length if diameter of its atom is $120\ pm?$
✓
Answer
Given: Type of unit cell is bcc.
Diameter of atom $=120 pm =120 \times 10^{-10} cm$
To find: Unit cell edge length (a)
Formula: For bcc unit cell, $r=\frac{\sqrt{3} a}{4}$
Calculation: Radius of atom $(r)=\frac{\text { Diameter of atom }}{2}$
$ =\frac{120 \times 10^{-10} cm }{2}$
$=60 \times 10^{-10} cm $
Using formula,
$ a =\frac{4 r }{\sqrt{3}}=\frac{4 \times 60 \times 10^{-10} cm }{1.732}$
$=1.386 \times 10^{-8} cm =138.6 pm $
Unit cell edge length is $138.6 pm$.
Diameter of atom $=120 pm =120 \times 10^{-10} cm$
To find: Unit cell edge length (a)
Formula: For bcc unit cell, $r=\frac{\sqrt{3} a}{4}$
Calculation: Radius of atom $(r)=\frac{\text { Diameter of atom }}{2}$
$ =\frac{120 \times 10^{-10} cm }{2}$
$=60 \times 10^{-10} cm $
Using formula,
$ a =\frac{4 r }{\sqrt{3}}=\frac{4 \times 60 \times 10^{-10} cm }{1.732}$
$=1.386 \times 10^{-8} cm =138.6 pm $
Unit cell edge length is $138.6 pm$.
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