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The Solid State

Question
CBSEENCH12011071
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A given metal crystallises out with a cubic structure having edge length of 361 pm. If there are four metal atoms in one unit cell, what is the radius of one atom.

  • 40 pm

  • 127 pm

  • 80 pm

  • 108 pm

Solution

B.

127 pm

Given, edge length = 361 pm
Four metal atoms in one unit cell
i.e effective number in unit cell (z) = 4 (given)
therefore,
It is a FCC structure
Face diagonal  = 4r

square root of 2 straight a end root space equals space 4 straight r space equals space straight r equals space fraction numerator square root of 2 space end root space straight x space 361 over denominator 4 end fraction space equals space 127 space pm

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