The Solid State

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Question
CBSEENCH12010755

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

  • 2a

  • 2 square root of 2 straight a
  • square root of 2 straight a end root
  • fraction numerator straight a over denominator square root of 2 end fraction

Solution

D.

fraction numerator straight a over denominator square root of 2 end fraction

In FCC unit cell atoms are in constant along face diagonal
So, √2a = 4R
therefore, the closest distance
left parenthesis 2 straight R right parenthesis space equals space fraction numerator square root of 2 straight a over denominator 2 end fraction space equals space fraction numerator straight a over denominator square root of 2 end fraction

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Question
CBSEENCH12010880

An ionic compound has a unit cell consisting of A ions at the corners of a cube and B ions on the centres of the faces of the cube. The empirical formula for this compound would be

  • A2B

  • AB

  • AB3

  • A3B

Solution

C.

AB3

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Question
CBSEENCH12010896

Based on lattice energy and other considerations which one of the following alkali metal chlorides is expected to have the highest melting point.

  • LiCl

  • NaCl

  • KCl

  • RbCl

Solution

B.

NaCl

Although lattice energy of LiCl higher than NaCl but LiCl is covalent in nature and NaCl ionic thereafter, the melting point decreases as we move NaCl because the lattice energy decreases as a size of alkali metal atom increases (lattice energy ∝ to melting point of alkali metal halide)

Question
CBSEENCH12010782

Copper crystallizes in fcc with a unit cell length of 361 pm. What is the radius of copper atom?

  • 108 pm

  • 127 pm

  • 157 pm

  • 181 pm 

Solution

B.

127 pm

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Question
CBSEENCH12010653

CsCl crystallises in body centred cubic lattice. If 'a' its edge length, then which of the following expression is correct?

  • straight r subscript Cs to the power of plus space plus straight r subscript Cl to the power of minus end subscript space equals space 3 straight a
  • straight r subscript Cs to the power of plus space plus straight r subscript Cl to the power of minus end subscript space equals space fraction numerator 3 straight a over denominator 2 end fraction
  • straight r subscript Cs to the power of plus space plus straight r subscript Cl to the power of minus end subscript space equals space fraction numerator square root of 3 over denominator 2 end fraction straight a
  • straight r subscript Cs to the power of plus space plus straight r subscript Cl to the power of minus end subscript space equals space square root of 3 straight a end root

Solution

C.

straight r subscript Cs to the power of plus space plus straight r subscript Cl to the power of minus end subscript space equals space fraction numerator square root of 3 over denominator 2 end fraction straight a

In CsCl, Cl- lie at corners of simple cube and Cs+ at the body centre, Hence, along the body diagonal, Cs+ and Cl- touch each other so
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