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Question
A compound crystallizes in bcc structure. What is unit cell edge length if diameter of its atom is 120 pm?
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Solution
Given: Type of unit cell is bcc.
Diameter of atom = 120 pm = 120 × 10-10 cm
To find: Unit cell edge length (a)
Formula: For bcc unit cell, r = `(sqrt3"a")/4`
Calculation: Radius of atom (r) = `"Diameter of atom"/2`
`= (120 xx 10^-10 "cm")/2`
= 60 × 10-10 cm
Using formula,
a = `(4"r")/sqrt3 = (4 xx 60 xx 10^-10 "cm")/1.732`
= 1.386 ×10-8 cm = 138.6 pm
Unit cell edge length is 138.6 pm.
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