Solving Solid State Physics: Max Wavelength of Po Crystal Diffraction

[kel]

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

 

[Kurdt]

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.

 

[m2003]

vin


Hello Kelvin,

You are on the right track with using the Bragg equation to solve this problem. The Bragg equation, 2d sin(angle) = n*wavelength, relates the spacing between crystal planes (d), the angle of incident/reflection (angle), the order of diffraction (n), and the wavelength of the radiation.

In this case, you are given the spacing between crystal planes (3.34A) and you need to find the maximum wavelength of radiation that can be diffracted from a powder of that crystal. To find the maximum wavelength, you need to consider the smallest possible value for the angle of incident/reflection. This occurs when the radiation is diffracted at an angle of 90 degrees. Therefore, your equation becomes 2d sin(90) = n*wavelength.

Since sin(90) = 1, the equation simplifies to 2d = n*wavelength. Now, to find the maximum wavelength, we need to consider the smallest possible value for n. This occurs when n = 1. Therefore, the maximum wavelength of radiation that can be diffracted from a powder of Po crystal is given by the equation 2(3.34A) = 1*wavelength. Solving for wavelength, we get a maximum wavelength of 6.68A.

I hope this helps. Keep in mind that in solid state physics, you will often need to use different equations and consider different factors depending on the specific problem. It takes practice and familiarity with the concepts to become comfortable with solving solid state physics problems. Keep at it and don't hesitate to ask for help when needed. Good luck!