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in a solid ab having nacl type structure a atom occupy the corner of the cubic unit cell and the face centered positions if all the face centered atom along one of thr axes are removed choose the correct options atomic weight of a =40 atomic weight of b = 60 ra=1.4a rb =2.8 a calculate density

in a solid ab having nacl type structure a atom occupy the corner of the cubic unit cell and the face centered positions if all the face centered atom along one of thr axes are removed choose the correct options atomic weight of a =40 atomic weight of b = 60 ra=1.4a rb =2.8 a calculate density
 

Grade:12th pass

1 Answers

Vasanth SR
askIITians Faculty 1335 Points
6 years ago
'AB' has NaCl structure, otherwise known as Rock salt structure. Hence one type of atoms must be arranged in FCC pattern (at all the 8 corners and all the 6 face centers) and other type of atoms must be present on all the 12 edges as well as at the center of the unit cell.

Since, 'A' atoms are occupying the corners of unit cell, they must also be arranged on the face centers. The B atoms can be found at the 12 edges and at the center of the unit cell as shown below.
536-599_q1-1.png
Therefore, before removing face centered atoms:

The number of 'A' atoms = (8 x 1/8) + (6 x 1/2) = 1 + 3 = 4[there are 8 'A' atoms at the corners and 6 'A' atoms at the face centers]

The number of 'B' atoms = (12 x 1/4) + (1 x 1) = 3 + 1 = 4[there are 12 'B' atoms at the edges and 1 'B' atom at the center of the unit cell]
However after removing two face centered 'A' atoms along one of the axes (x axis) as shown below :
536-88_q1-2.png
The number of 'A' atoms = (8 x 1/8) + (4x 1/2) = 1 + 2 = 3[there are now only 4 'A' atoms at the face centers]

The number of 'B' atoms = (12 x 1/4) + (1 x 1) = 3 + 1 = 4

Therefore the stoichiometry after removing these atoms is: A3B4

Note:

Each atom at the corner contributes 1/8th, and each atom at the face center contributes 1/2nd and each atom along the edge contributes 1/4th to the unit cell.

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