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A compound crystallizes in bcc structure. What is unit cell edge length if diameter of its atom is 120 pm?

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प्रश्न

A compound crystallizes in bcc structure. What is unit cell edge length if diameter of its atom is 120 pm?

योग
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उत्तर

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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