Bragg Scattering - Need help because it is hard for me.

[getcarter]

I am really stuck on this problem. This entire section I have been teaching myself using the homework answers but I have no idea where to start. Thanks anyone.

Question:
A beam of thermal neutrons emerges from a nuclear reactor and is incident on a crystal as shown below. The beam is Bragg scattered from a crystal whose scattering planes are separated by 0.247nm. From the continuous energy spectrum of the beam we wish to select neutrons of energy 0.0105eV. Find the Bragg scattering angle that results in a scattered beam of this energy. Will other energies also be present in this scattered beam?
http://qaboard.cramster.com/answer-board/image/373f241a0a260e4f6fd216bbcb88754a.jpg

Homework Statement

d = 0.247 nm
E of neurons 0.0105ev

Homework Equations

http://earth.esa.int/applications/data_util/SARDOCS/_icons/c3_bragg.jpg

http://earth.esa.int/applications/data_util/SARDOCS/_icons/c3_brag_formula.jpg
http://earth.esa.int/applications/data_util/SARDOCS/_icons/c3_brag_formula1.jpg

The Attempt at a Solution

2dsin(tetha) = n(lamda)
from here sin(tetha) comes.

 

[phz]

Calculate the wave-length of the neutron through the de Broglie-relation. Then use the Bragg condition to identify the angle.

 

[thomate1]

but what is n?




Firstly, I understand that you are struggling with the concept of Bragg scattering and how to apply it in this specific problem. Don't worry, it can be a difficult concept to grasp at first. I would suggest seeking help from a professor or a tutor who can guide you through the steps and explain the underlying principles to you. Alternatively, you can also refer to textbooks or online resources for a detailed explanation of Bragg scattering.

To answer your question, n in the equation 2dsin(theta) = n(lambda) represents the order of the diffraction. In this case, since it is not mentioned, we can assume that n=1. Now, to find the Bragg scattering angle, we can rearrange the equation to get sin(theta) = (n*lambda)/(2d). Plugging in the values, we get sin(theta) = (1*0.0105eV)/(2*0.247nm). You can convert the energy unit to Joules and the distance unit to meters for convenience. Once you have the value of sin(theta), you can use a scientific calculator to find the value of theta.

As for the second part of the question, yes, there will be other energies present in the scattered beam. This is because the beam is not monochromatic (having only one wavelength/energy) and the crystal will diffract all the wavelengths/energies that are incident on it. However, the intensity of the scattered beam will be highest at the specific Bragg scattering angle that you have calculated.

I hope this helps you in understanding the problem better. Keep practicing and seeking help when needed. Good luck!