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Question

Atoms of element B from the HCP lattice and those of element A occupy 23 rd of tetrahedral voids. What is the formula of the compound formed by the elements A and B?


A

A1B1

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B

A2B1

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C

A3B2

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D

A4B3

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Solution

The correct option is D

A4B3


Explanation for correct option:

(D) A4B3

Step 1: Calculation of number of atoms in unit clell

  • Given that, atoms of B form an hcp lattice. So, the atoms at corners are shared by 6 unit cells. So, its contribution is16; Face centred atoms contribute12 and middle layer atoms contribute 1 each.
  • So, the effective number of atoms in a unit cell =16×12+12×2+1×3

=2+1+3=6

Step 2: Calculation of the number of tetrahedral voids:

Numberoftetrahedralvoids=2×Numberofatomsformingthelattice.Numberoftetrahedralvoids=2×6=12

Step 3: Finding the formula:

  • So, the number of atoms of A=23x12

=8

  • Number of atoms of B=6

So,A:BA:B8:64:3

  • So, the formula is A4B3. This is the correct option.

Explanation for incorrect option:

(A) A1B1

  • The obtained formula does not match the above option. So, this is an incorrect option.

(B) A2B1

  • The obtained formula does not match the above option. So, this is an incorrect option.

(C) A3B2

  • The obtained formula does not match the above option. So, this is an incorrect option.

Hence, the correct option is (D) A4B3.


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