Crystal structure and diffraction

[math_04]

Homework Statement

You wish to study a crystal's structure by diffracting thermal, non relativistic neutrons from the crystal, so you go to a nuclear reactor and set up your diffraction experiment on one of the neutron beam lines. The neutrons emerge from the reactor with a range of wavelengths (ie a range of energies/momenta) so you use a chopper to select neutrons of a certain wavelength.

The simplest chopper consists of two disks made from a highly neutron absorbing material mounted on an axle. The disks are 2m apart. In each disk is a small slot (to let the neutrons through). There is an offset of 10 degs between the two slots and the chopper rotates rapidly.

The distance between the planes of atoms in the diffracting crystal is 1.73 Arnstrongs and you observe strong diffraction when the angle of incidence and diffracted neutron beams is 163 degs. Calculate the minimum rotational speed of the chopper in revolutions/minute.

Homework Equations

Braggs law : n*lamda = 2d * sin theta

The Attempt at a Solution

using theta = 180-163/2 = 8.5 and plugging in other values (d= 1.73 X 10^-10 m and n=1)

I got lamda = 5.11*10^-11 m.

Im not sure that my theta value is right and secondly, I have no idea how the experiment works. How do the choppers choose the wavelength of light and any hints on how to proceed?

Thanks.

 

[Jhero]

your first step would be to confirm the accuracy of the given information and equations. It is important to double check all values and equations before proceeding with the calculation.

Assuming the given values and equations are accurate, your approach seems correct. The angle of incidence and diffraction can be calculated using Bragg's law and the known distance between the planes of atoms. The selected neutron wavelength can then be used to determine the minimum rotational speed of the chopper.

However, it is important to note that the chopper does not choose the wavelength of the neutrons. The purpose of the chopper is to select neutrons of a certain wavelength by blocking out all other wavelengths. This is achieved by the offset between the two slots on the disks, which allows only a specific wavelength of neutrons to pass through.

To proceed with the calculation, you can use the formula for rotational speed: revolutions/minute = (2*pi)/time, where time is the time taken for one complete rotation of the chopper. The minimum rotational speed can then be calculated using the selected neutron wavelength and the distance between the two disks on the chopper.

It is also important to consider any other factors that may affect the experiment, such as the neutron flux from the reactor and the efficiency of the chopper in selecting the desired wavelength. These factors may need to be taken into account for a more accurate calculation.

Overall, as a scientist, it is important to have a thorough understanding of the experiment and all the variables involved in order to accurately calculate the minimum rotational speed of the chopper.