Solving Solid State Physics: Max Wavelength of Po Crystal Diffraction

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SUMMARY

The discussion focuses on calculating the maximum wavelength of radiation diffracted from a polonium (Po) crystal with a simple cubic structure and a lattice spacing of 3.34 Å. The Bragg equation, 2d sin(angle) = n*wavelength, is identified as the relevant formula for this calculation. The key insight provided is that to maximize the wavelength, one should consider the angle that maximizes sin(theta), which is 1, corresponding to an angle of 90 degrees. This leads to the conclusion that the maximum wavelength is equal to twice the lattice spacing.

PREREQUISITES
  • Understanding of Bragg's Law in solid state physics
  • Familiarity with crystal structures, specifically simple cubic lattices
  • Knowledge of wavelength and diffraction concepts
  • Basic trigonometry, particularly sine functions
NEXT STEPS
  • Study the derivation and applications of Bragg's Law in solid state physics
  • Explore the properties of simple cubic crystal structures and their implications on diffraction
  • Learn about the relationship between lattice spacing and diffraction patterns
  • Investigate other diffraction techniques and their mathematical foundations
USEFUL FOR

This discussion is beneficial for students and researchers in solid state physics, particularly those studying crystal diffraction and the properties of materials like polonium.

kel
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Homework Statement



The element Po forms a crystal with a simple cubic structure of spacing
(3.34A). What is the maximal wavelength of radiation that is diffracted from a powder of that crystal

Homework Equations


N/a, however I thought that it may well be something to do with the bragg equation i.e 2d sin(angle) = n*wavelength


The Attempt at a Solution



I had started using the bragg equation, but it's fairly obvious to see that I need to have the angle of incident/reflection also in order to find the wavelength.

As this is the first time that I have had any experience of solid state, I'm really not quite getting it - probably just me.

Could you suggest where I may be going wrong i.e. am I using the wrong equation for this question? and could you suggest a starting point.

I guess that I need to use some feature of the cubic structure in order to calculate this, but I'm a bit lost.

Thanks
Kel
 
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The question asks for the maximum wavelength and so all you have to do is think of what sin theta will give you the largest value.
 

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