# A question regarding particle diffraction - Might have posted in wrong place?

• BruceSpringste
In summary, the problem involves finding the angles at which a beam of neutrons with a variety of energies can be diffracted to obtain neutrons with a specific energy of 0.050 eV. Using the non-relativistic equation for kinetic energy and de Broglie's law, we can find the wavelength of the neutrons and use Bragg's law to calculate the angles at which they will be diffracted. The key is to remember that kinetic energy can be written as p^2/2m, where p is the momentum of the neutrons. If stuck, show your work for further assistance.
BruceSpringste

## Homework Statement

"A beam of neutrons that emerges from a nuclear reactor contains neutrons with a variety of energies. To obtain neutrons with an energy of 0.050 eV, the beam is passed through a crystal whose atomic planes are 0.20 nm apart. At what angles relative to the original beam will the desired netruons be diffracted?"

## Homework Equations

Braggs law
mλ=sin2θ

3. The Attempt at a Solution [/b
My first thought was to use braggs law and simply solve for θ and m=1,2,3... but θ>90degrees.
However the problem seems a lot more complex than that. My book doesn't have any answers to the question so I can't double check if I have done this right!

BruceSpringste said:

## Homework Statement

"A beam of neutrons that emerges from a nuclear reactor contains neutrons with a variety of energies. To obtain neutrons with an energy of 0.050 eV, the beam is passed through a crystal whose atomic planes are 0.20 nm apart. At what angles relative to the original beam will the desired netruons be diffracted?"

## Homework Equations

Braggs law
mλ=sin2θ3. The Attempt at a Solution [/b
My first thought was to use braggs law and simply solve for θ and m=1,2,3... but θ>90degrees.
However the problem seems a lot more complex than that. My book doesn't have any answers to the question so I can't double check if I have done this right!

The expression you wrote for Bragg's law is not correct. It should be

$$m\lambda = 2d \sin\theta .$$

Does using that expression give you reasonable answers? By the way, the original (incorrect) expression you wrote for Bragg's law did not contain the plane spacing d. Was that a typo, or did you not notice that you weren't using the plane spacing in your calculation? It's handy to keep track of what pieces of information you have but didn't use so that you can perform a 'sanity check' and assess whether or not you think you should have used that piece of information in your calculation.

I of course meant what you wrote. It was a typo!

And no it doesn't feel like I get a reasonable answer. It feels like something is missing.

Since the neutrons are behaving like a wave I thought using braggs law would solve it for me.
However the problem is my book doenst provide any answers to the questions. And i was wondering if I have been thinking correctly!

Last edited:
BruceSpringste said:
I of course meant what you wrote. It was a typo!

They're not always typos! Sometimes people just have the wrong equation, so we have to double-check that first.

And no it doesn't feel like I get a reasonable answer. It feels like something is missing.

Since the neutrons are behaving like a wave I thought using braggs law would solve it for me.
However the problem is my book doenst provide any answers to the questions. And i was wondering if I have been thinking correctly!

Bragg's law does seem like the appropriate approach to the problem. Have you double checked all of the numbers you were given and their units? For example, are you sure the neutron energy is not supposed to be in MeV? That would give a more reasonable wavelength (on the order of ~ 0.1 nm) for the neutrons.

Haha I get that! And I'm very grateful that you're taking your time to answer this question.

The unit is eV, I have double checked.
To obtain lambda I feel I have to use de broglies equation: λ=h/γmv
Since 0.050 eV is small compared with its rest energy mc^2 I figured Y=1.
However from this point I am stuck!

mv^2/2 = KE
v=√(2mKE)
m = mass of a neutron
E = ? Neutrons do not have an electrif fieldbecause they are neutral. But it can't be 0?
K = 0.05 eV

Last edited:
BruceSpringste said:
Haha I get that! And I'm very grateful that you're taking your time to answer this question.

The unit is eV, I have double checked.
To obtain lambda I feel I have to use de broglies equation: λ=h/γmv
Since 0.050 eV is small compared with its rest energy mc^2 I figured Y=1.
However from this point I am stuck!

mv^2/2 = KE
v=√(2mKE)
m = mass of a neutron
E = ? Neutrons do not have an electrif fieldbecause they are neutral. But it can't be 0?
K = 0.05 eV

Hm, before I wasn't getting reasonable answers either, but I did it again and I get something that looks ok, so I'll assume I'm more correct this time. So, let's start with your suggestions. I agree that since the kinetic energy of the neutron is much smaller than its rest mass energy, that ##\gamma## is probably close to 1, which means we can use the non-relativistic equation for the kinetic energy.

I also agree that you will need to use de Broglie's law, ##\lambda = h/p##, where p = mv if we can use the non-relativistic equations.

Now, I'm not sure what you mean by E here, but electric field doesn't come into this problem at all. Instead, I would suggest you look at the equations you wrote down again. You want to find ##\lambda##, yes? Do you have enough information to find it from the equations you wrote down for kinetic energy and de Broglie's law?

Also, I'll give you a hint that may save you some algebra: you can write the kinetic energy as

$$KE = \frac{p^2}{2m}.$$

(You can derive this from the usual form KE = mv^2/2 by plugging in v = p/m).

So, see if you can solve the problem now, and if you get stuck again show us your work and we'll try to point out where you went wrong (if you did) or give you some hints to get you unstuck.

## 1. What is particle diffraction?

Particle diffraction is a phenomenon in which particles, such as electrons or protons, exhibit wave-like behavior when passing through a narrow slit or around an object.

## 2. Why is particle diffraction important?

Particle diffraction is important because it provides evidence for the wave-particle duality of matter, which is a fundamental concept in quantum mechanics. It also has practical applications in various fields, such as particle physics, materials science, and medical imaging.

## 3. How does particle diffraction occur?

Particle diffraction occurs when a wave-like disturbance, such as an electromagnetic wave or a matter wave, encounters an obstacle or a narrow opening. The wave is then diffracted, or spread out, as it passes through the opening, resulting in a diffraction pattern.

## 4. Can particle diffraction be observed with the naked eye?

No, particle diffraction cannot be observed with the naked eye because it occurs on a very small scale, at the level of individual particles. Specialized equipment, such as an electron microscope, is needed to observe and measure particle diffraction.

## 5. Is particle diffraction the same as wave interference?

No, particle diffraction and wave interference are two different phenomena. While both involve the interaction of waves, particle diffraction is caused by the bending of waves around obstacles, whereas wave interference occurs when two or more waves interact with each other to produce a new wave pattern.

• Introductory Physics Homework Help
Replies
1
Views
2K
Replies
4
Views
5K
Replies
1
Views
2K
Replies
5
Views
6K
• Introductory Physics Homework Help
Replies
1
Views
1K
• Atomic and Condensed Matter
Replies
16
Views
2K
Replies
5
Views
2K
• Introductory Physics Homework Help
Replies
8
Views
9K
• Introductory Physics Homework Help
Replies
2
Views
3K
• Introductory Physics Homework Help
Replies
2
Views
2K