Distance between 2 atoms in a crystal

In summary, the conversation discusses the calculation of the shortest distance between two adjacent atoms in a crystal with a density of 9.2*10^3 and a total of 27 atoms with a mass of 3.5*10^-25 each. After discussing various attempts at a solution, it is determined that the correct answer is 3.4*10^-10, as the volume and density of the crystal are specific to this arrangement of 27 atoms.
  • #1
Nemo's
69
0

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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  • #2
do you thinkthis is the correct answer?
 
  • #3
I think your "correct answer" is off by 10
 
  • #4
L is correct. Should you really be dividing by 2?
 
  • #5
Sorry the correct answer should be 3.4*10^-10
Should I divide by 3 then ? Why ?
 
  • #6
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.
 
  • #7
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
 
  • #8
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
 

Attachments

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  • #9
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.
 

Related to Distance between 2 atoms in a crystal

1. What is the distance between two atoms in a crystal?

The distance between two atoms in a crystal can vary depending on the type of crystal and the arrangement of atoms within it. Generally, this distance ranges from 0.1 to 0.3 nanometers.

2. How is the distance between two atoms in a crystal measured?

The distance between two atoms in a crystal is typically measured using X-ray crystallography, a technique that involves directing X-rays at the crystal and analyzing the resulting diffraction pattern.

3. Can the distance between two atoms in a crystal change?

Yes, the distance between two atoms in a crystal can change due to various factors such as temperature, pressure, and the presence of other atoms or molecules. This can affect the physical and chemical properties of the crystal.

4. What is the significance of the distance between two atoms in a crystal?

The distance between two atoms in a crystal is significant because it determines the strength and stability of the crystal's structure. It also affects the interactions between atoms and can influence the properties of the crystal, such as its melting point and electrical conductivity.

5. How does the distance between two atoms in a crystal affect its properties?

The distance between two atoms in a crystal can affect its properties in various ways. For example, a shorter distance between atoms can result in a stronger and more rigid crystal, while a longer distance can lead to a weaker and more flexible crystal. It can also affect the optical, thermal, and electrical properties of the crystal.

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