Distance between 2 atoms in a crystal

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Homework Help Overview

The discussion revolves around calculating the shortest distance between the centers of two adjacent atoms in a crystal structure, specifically a cube containing 27 atoms. The problem involves concepts of density, mass, and volume in the context of atomic arrangements.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the relationship between density, mass, and volume, questioning the method of calculating distances based on the arrangement of atoms. There are discussions about whether to divide by 2 or 3 and the implications of how atoms are positioned within the crystal structure.

Discussion Status

The discussion is active with participants questioning the validity of the initial calculations and interpretations of the problem. Some guidance has been offered regarding the arrangement of atoms and the implications of density in relation to the specific crystal structure being analyzed.

Contextual Notes

There is uncertainty regarding the interpretation of density as it applies to a small crystal of 27 atoms, as opposed to a larger sample. Participants are considering how the arrangement of atoms affects the calculated distances.

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Homework Statement



Given a crystal (cube) with regularly arranged atoms (Total 27 atoms)
The mass of each atom is 3.5*10^-25. The density of the crystal is 9.2*10^3
What is the shortest distance between the centres of two adjacent atoms?

Homework Equations



density = mass / volume

The Attempt at a Solution



Volume= (27*3.5*10^-25)/(9.2*10^3)=1.03*10^-27
Length(L)=1*10-9
Distance between two atoms is L/2=5.04*10^-10
Correct answer is 3.4*10^-9
 
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do you thinkthis is the correct answer?
 
I think your "correct answer" is off by 10
 
L is correct. Should you really be dividing by 2?
 
Sorry the correct answer should be 3.4*10^-10
Should I divide by 3 then ? Why ?
 
What you probably did was to assume the volume of 27 atoms had an atom at every corner and one between. But if you put this volume next to another, the atoms on the edges would be to close. In fact, the distance should be 3.
 
barryj said:
But if you put this volume next to another, the atoms on the edges would be to close.
So the atoms on the edges would be closer than others and that's the required "shortest distance"?
I just can't really imagine what it looks like
 
Maybe I wasn't clear. Put the atoms in a uniform rectangular three dimensional grid. My attachment shows the top view. Notice the volume is (3d)^3
 

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The difficulty is, what does volume (and therefore density) mean when applied to a crystal consisting of only 27 atoms? It does not say that the density given is for arbitrarily large chunks of this material - it is for specifically this crystal of 27 atoms. So I tend to agree with Nemo's answer.
 
  • #10
Good point, I guess whoever stated the "correct answer" thought it was for a large chunk.
 

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