A body-centered cubic unit cell has a volume of 2.17×10−23 cm3 . Find the radius of...

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Question

A body-centered cubic unit cell has a volume of 2.17×10−23 cm3 . Find the radius of the atom in pm.

Answer 1

Answer #1

Determine the edge length of the unit cell:

[cube root of] 2.583 x 10¯²³ cm³ = 2.789 x 10¯⁸ cm

We wish to determine the value of 4r, from which we will obtain r, the radius of the atom. Using the Pythagorean Theorem, we can find:

d² + (d√2)² = (4r)²

3d² = (4r)²

3(2.789 x 10¯⁸ cm)² = 16r²

r = 1.207 x 10¯⁸ cm

Radius of the atom = 120.777 pm

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Answer 2

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