What Is the Bragg Scattering Angle for Thermal Neutrons with 0.0105 eV Energy?

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Homework Help Overview

The discussion revolves around the Bragg scattering of thermal neutrons with a specific energy of 0.0105 eV incident on a crystal with scattering planes separated by 0.247 nm. Participants are exploring the implications of this setup on the scattering angle and the presence of other energies in the scattered beams.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to calculate the Bragg scattering angle using a specific equation and questions whether other energies will also be present in the scattered beams. Some participants discuss Bragg's formula and the concept of higher order reflections, suggesting that multiple wavelengths and corresponding energies may be involved.

Discussion Status

Participants are actively engaging with the problem, with some providing calculations and others seeking clarification on the implications of their findings. There is a recognition of the possibility of multiple energies being present in the scattered beams, but no consensus has been reached on the specifics.

Contextual Notes

Participants are navigating the complexities of Bragg's law and the implications of scattering angles, while also addressing the nature of energy states in the context of neutron scattering.

tan90
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A beam of thermal neutrons emerges from a nuclear reactor and is incident on a crystal. The beam is Bragg scattered from crystal whose scattering planes are separated by 0.247 nm. From the continuous energy spectrum of the beam we wish to select neutrons of energy 0.0105 eV. Find the Bragg scattering angle that results in a scattered beam of this energy. Will other energies also be present in the scattered beams?
 
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so what i did was i have d =0.247 nm and K = 0.0105 eV. I used the equation 2dsin(theta) = hc/ sqrt( 2(mc^2) K). and then I got theta = 34.4 degrees. So, it asks if other energies will also be present in the scattered beams and I am not quite sure about that but my guess would be yes. would anyone please help me understand this?
 
Bragg's formula is
2*d*sin(theta)=n*lambda

Keeping the angle fixed, it will be satisfied by various wavelengths, corresponding to various values of n.
Your value is for n=1 but you can have higher order reflections of other wavelengths (that will be different energies for neutrons)
 
thanks a lot.
i was thinking the same but didn't know how to express it.
 
I have another question. So, an electron bounces elastically back and forth in one dimension between two walls that are L apart. Assuming that the electron is represented by a de Broglie standing wave with a node at each wall, show that the permitted de Broglie wavelengths are lambda = 2L/n where n =1,2,3...
What I don't understand here is why is lambda = 2L/n but not L/n ?
I would really appreciate if anyone would help me with this.
 
If you have nodes at the walls, you need to fit an integer number of half-wavelengths between the walls. The distance between two nodes is wavelength/2.
L=n (lambda/d)
 

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