Help Me Solve a Lab Question Involving Atoms in a Lattice

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SUMMARY

The discussion focuses on solving a lab question regarding the arrangement of spherical atoms in a cube closest-packed lattice and a body-centered cubic structure. The first part requires calculating the total number of atoms within a small cube constructed at the corners of the lattice, determining the volume occupied by these atoms, the volume of the cube, and the fraction of space occupied. The second part asserts that in a body-centered cubic structure, 68.0 percent of the available space is occupied by atoms, necessitating a similar cube construction for verification.

PREREQUISITES
  • Understanding of cubic lattice structures
  • Knowledge of atomic packing and volume calculations
  • Familiarity with spherical geometry
  • Basic principles of solid-state physics
NEXT STEPS
  • Study atomic packing factors in different lattice structures
  • Learn how to calculate volumes of spheres and cubes
  • Explore the concept of space-filling in crystal lattices
  • Investigate the properties of body-centered cubic lattices
USEFUL FOR

Students in physics or materials science, educators teaching solid-state physics, and anyone involved in crystallography or atomic structure analysis.

cyks07
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this is one of lab question but i don't even understand please help me
the question is

1. consider spherical atoms of radius R arranged in a cube closest-packed lattice. if a small cube is constructed so that its corners are at the centers of the corner atoms, then one-eighth of each corner atom and one-half of each face-centered atom lies within the small cube. what is the total number of atoms within the small cube? calculate the volume occupied by these atoms, the volume of the cube, and the fraction of the available space that is occupied by atoms.


2. show that for spherical atoms in a body-centered cubic structure exactly 68.0 percent of the available space is occupied by atoms. (hint : begin by constructing cube like the one described in question 1

please..if u know help me
 
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nobody knows?
 
This question belongs in the homework section, also, you're going to need to show your analysis for each of them before any of us are allowed to help you. It's just the policy here at physicsforums.
 

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