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JEE Main 20172 April
Exam
JEE Main
Year
2017
Date
2 April
Subject
Chemistry
Chapter
Solid State

JEE Main 2017 · 2 April · Chemistry · Solid State

A metal crystallizes in a face centred cubic structure. If the edge...

A metal crystallizes in a face centred cubic structure. If the edge length of its unit cell is ′a′' a ', the closest approach between two atoms in the metallic crystal will be

Options

  1. A22a2\sqrt{2}a
  2. B2a\sqrt{2}a
  3. Ca2\dfrac{a}{\sqrt{2}}
  4. D2a2a

Correct answer

C. a2\dfrac{a}{\sqrt{2}}

Step-by-step solution

FCCFCCunit cell: eight corners with six faces

r+2r+r=2a4r=2aClosestdistanceinfcc2r=2a2=2a2×2=a2r + 2r + r = \sqrt{2}a4r = \sqrt{2}aClosestdistanceinfcc2r = \dfrac{\sqrt{2}a}{2} = \dfrac{\sqrt{2}a}{\sqrt{2} \times \sqrt{2}} = \dfrac{a}{\sqrt{2}}

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