How Do You Calculate Atomic Plane Spacing in a Cleaved Crystal?

[bang911]

I just had my first college physics class today, and already I'm stuck on the first problem. I already had physics in HS and I expected I wouldn't have that much trouble in college. So here is a question that I have no clue how to answer.

A crystalline solid consists of atoms stacked up in a repeating lattice structure. Consider a crystal as shown in figure p1. The atoms reside at the corners of the cubes of side L = 0.200 nm. One piece of evidence for the regular arrangement of atoms comes from the flat surfaces along which a crystal separates, or cleaves, when it is broken. Suppose this crystal cleaves along a face diagonal as in p2. Calculate the spacing d between two adjacent atomic planes that separate when the crystal cleaves.

(the pictures are in 3d)

OOOOOOOO
OOOOOOOO
OOOOOOOO
l<-L->l \d\



OO OOOOOO
OOO OOOOO
OOOO OOOO



the answer is .141 nm

so if anyone would help me out with this i would greatly appreciate it

 

[ehild]

A crystalline solid consists of atoms stacked up in a repeating lattice structure. Consider a crystal as shown in figure p1. The atoms reside at the corners of the cubes of side L = 0.200 nm. One piece of evidence for the regular arrangement of atoms comes from the flat surfaces along which a crystal separates, or cleaves, when it is broken. Suppose this crystal cleaves along a face diagonal as in p2. Calculate the spacing d between two adjacent atomic planes that separate when the crystal cleaves.

(the pictures are in 3d)

Well, maybe my picture helps.

ehild

 

[JasonRox]

Yeah, that picture is helpful.

 

[da_willem]

Just use the Pythagorean theorem

 

[bang911]

Ya I had no clue how the pythagorean theorem was to be used when i read the problem. Thanks for the post and that nice diagram though. Doesn't seem tough any more.

 

[ehild]

Ya I had no clue how the pythagorean theorem was to be used when i read the problem. Thanks for the post and that nice diagram though. Doesn't seem tough any more.

It's a pleasure ...

ehild