How to Calculate the Shortest Distance Between Atoms in a BCC Structure?

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SUMMARY

The discussion focuses on calculating the shortest distance between neighboring atoms in a body-centered cubic (BCC) structure of barium, with a cell edge length of 0.5025 nm. Participants suggest using geometric relationships to derive the bond lengths, emphasizing the importance of visualizing the atomic arrangement. The calculation involves recognizing the triangular geometry formed by the atoms and applying ratios to determine the distances. Bragg's law is deemed unnecessary due to the lack of specific angle and wavelength information.

PREREQUISITES
  • Understanding of body-centered cubic (BCC) crystal structures
  • Familiarity with basic geometry and triangle properties
  • Knowledge of Avogadro's number and its application in calculations
  • Ability to interpret atomic arrangements in crystallography
NEXT STEPS
  • Study the geometric properties of body-centered cubic (BCC) structures
  • Learn how to calculate bond lengths using geometric ratios
  • Explore crystallography concepts related to atomic distances
  • Review Avogadro's number and its significance in solid-state physics
USEFUL FOR

Chemistry students, materials scientists, and anyone interested in solid-state physics and crystallography will benefit from this discussion.

vipertongn
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Homework Statement



Barium crystallizes in a body centered cubic structure in which the cell edge length is 0.5025 nm. Calculate the shortest distance between neighboring atoms in the crystal.

Homework Equations



Avagodro's number

The Attempt at a Solution



0.5025 x 10^-7 cm ( 1/2atoms) (6.022 x 10^23 atoms)

That's as much as I know so far, I can't use bragg's law because I don't have the angle nor the order nor the wavelength to figure it out. How should I solve this?
 
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Hi vipertongn! :smile:

I don't know what body centered cubic structure or cell edge length is,

but this looks like a simple geometry problem to me …

they've given you the geometrical pattern and one length, and you have to calculate another length. :wink:
 
http://cst-www.nrl.navy.mil/lattice/struk.picts/a2.s.png

See if you can visualize the triangle...You know the triangle sides. Now calculate the bond lengths from ratios of the triangles.
 
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