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  4. In a hypothetical solid, C atoms are found to form cubical close-packed lattice. A atoms occupy all tetrahedral voids and B atoms occupy all octahedral voids. <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/c-pl4kupv2nri9.png /> A and B atoms are of appropriate size, so that there is no distortion in the CCP lattice of C atoms. Now, if a plane as shown in the following figure is cut, then the cross section of this plane will look like

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Q. In a hypothetical solid, C atoms are found to form cubical close-packed lattice. A atoms occupy all tetrahedral voids and B atoms occupy all octahedral voids.

Question

A and B atoms are of appropriate size, so that there is no distortion in the CCP lattice of C atoms. Now, if a plane as shown in the following figure is cut, then the cross section of this plane will look like

NTA AbhyasNTA Abhyas 2020The Solid State

Solution:

From figure, it is clear that 4 corners and 2 face centers lie on the shaded plane. Therefore, there will be six C atoms, and atoms (marked A) in TVs do not touch other.

Fig (i) is not possible; four atom marked C.

Fig. (ii) is not possible, atoms A in TVs are not shown in figure.

Fig. (iii) is possible, since atoms A in TVs are not touching each other. There are four atoms A on two body diagonals contained in shades plane.

Fig (iv) is not possible, since atoms A in TVs are touching each other.