Interatomic spacing problem

[Idan9988]

Homework Statement

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Relevant Equations

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according to the figure, it's look like d is the distance between the center of two adjacent atoms, and so it should be simply L. I don't understand what d represents in the figure.
that's the solution:

Even if d is half the distance between two adjacent atoms that positioned diagonally (I don't see why), is came out to me completely different expression:

 

[kuruman]

If the interatomic separation is $L$ (see figure below) what is the separation between the planes indicated by the solid black lines? That is how you identify what you are being asked. Note that the figure shows a different cleavage plane from the one given to you but the idea is the same.

 

[Idan9988]

but if the interatomic separation is L, and what I'm being asked about is the distance between those parallel lines, isn't d should be equal simply to L?

 

[Idan9988]

according to the answer, d is half the distance between two diagonally positioned atoms, which in the figure is the line segment between one atom to the red arrow. I don't see why this segment is the answer to what I'm being asked about?

 

[Lnewqban]

according to the answer, d is half the distance between two diagonally positioned atoms, which in the figure is the line segment between one atom to the red arrow. I don't see why this segment is the answer to what I'm being asked about?

 

[kuruman]

but if the interatomic separation is L, and what I'm being asked about is the distance between those parallel lines, isn't d should be equal simply to L?

Draw a line that is perpendicular to the two parallel lines. The distance $d$ between them is the segment of the perpendicular contained between the two.