Question

The miller indices of two parallel planes is a crystal are:
A.Same
B.Different

Answer 1

Hint:Miller indices is a set or group of three numbers that indicates the orientation of a plane or a set of parallel planes of atoms in a crystal. These miller indices form a notation system in crystallography for planes in crystal lattices.


Complete step by step answer:
Miller indices are determined by the intersection of the plane with axes. The reciprocals of these intercepts are calculated, the fraction gives out the three miller indices\[\left( {hkl} \right)\]. For instances now, a plane parallel to two axis and cuts the third axis at the length equal to one edge of a unit cell will have miller indices of $\left( {100} \right),\left( {010} \right),$ or $\left( {001} \right)$ depending upon the axis cut. And the plane cutting all three axes at the length equal to the edges of the unit cell will have miller indices of $\left( {111} \right)$.
As of the question, the miller indices of two parallel planes in a crystal are the same because they are equally spaced parallel planes, so therefore the miller indices of equally spaced parallel planes are the same. As we know, miller indices does not only define a particular plane but also define a set of parallel planes. The planes whose intercepts are $\left( {1,1,1} \right)$,$\left( {3,3,3} \right)$,$\left( { - 2, - 2, - 2} \right)$ are all represented by the same miller indices.
The correct option for the question is (A).

Additional information: The word unit cell means, the smallest group of atoms which makes the overall symmetry of a crystal, the entire lattice can be built up by repetition in three dimensions.
If each atom in the crystal is represented by a point and these points are connected through lines, now the resulting lattice may get divided into a number of identical blocks or unit cells, the intersecting edges of one of the unit cells defining crystallographic axes.

Note:
The concept of miller indices is easily understandable but only with the knowledge of basic words associated with it like unit cell, parallel lines, intercepts, and the knowledge of how it is the same and different.