# Finding shortest distance in bcc

• vipertongn
In summary, the problem is to calculate the shortest distance between neighboring atoms in a barium crystal with a body centered cubic structure and a cell edge length of 0.5025 nm. This can be solved using basic geometry principles and the known values of the cell edge length and Avagodro's number.
vipertongn

## 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?

Hi vipertongn!

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.

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.

Last edited by a moderator:

## 1. What is a bcc structure?

A bcc (body-centered cubic) structure is a type of crystal structure commonly found in metals and alloys. In this structure, each atom is located at the center of a cube and is surrounded by 8 other atoms at the corners of the cube. This results in a high packing efficiency and strength in the material.

## 2. Why is finding the shortest distance in bcc important?

Knowing the shortest distance between atoms in a bcc structure is crucial for understanding the properties and behavior of the material. It can also aid in designing and predicting the performance of bcc materials in various applications.

## 3. How do you calculate the shortest distance between atoms in a bcc structure?

The shortest distance between atoms in a bcc structure can be calculated using the lattice parameter and the Miller indices of the crystal plane. This can be done using mathematical formulas and equations specific to bcc structures.

## 4. What factors can affect the shortest distance in a bcc structure?

The shortest distance between atoms in a bcc structure can be influenced by factors such as temperature, pressure, and the presence of defects or impurities in the material. These conditions can cause changes in the lattice parameter, which in turn affects the shortest distance between atoms.

## 5. How is the shortest distance in bcc determined experimentally?

The shortest distance between atoms in a bcc structure can be measured experimentally using techniques such as X-ray diffraction or electron microscopy. These methods allow for the visualization and measurement of the atomic structure, providing an accurate determination of the shortest distance between atoms in a bcc material.

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