Electrons impinging on a crystal

In summary, the conversation discusses using the crystal spacing and Bragg's law formula to calculate the wavelength and kinetic energy of electrons. It is noted that an interference pattern can be observed for n=1 with small θ and the problem is asking for an approximate answer. The speaker suggests using a value of λ=0.4nm to get an energy of 10 eV.
  • #1
tanaygupta2000
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Homework Statement
Under certain conditions, a beam of electrons impinging on a crystal surface will diffract and a
scattering pattern of the beam can be obtained. What is the approximate kinetic energy of the electrons needed in order to the see the pattern?
(Assume the lattice spacing of the crystal to be 0.4 nm)
(a) 100 eV (b) 1 eV (c) 0.1 eV (d) 10 eV
Relevant Equations
Bragg's law. 2d sinθ = nλ
De-broglie wavelength, λ = h/p
Since the crystal spacing is given to be 0.4 nm, so d = 0.4 nm = 4e-10 m in Bragg's law formula
For θ = 90° & n = 1, I got λ = 2d = 8e-10 m

Using this value in De-broglie wavelength, I got p = h/λ = 8.28e-25

Now kinetic energy of the electrons is given by E = p^2/2m
Using value of p, I am getting E = 2.35 eV, which doesn't seem to match any option.
Where am I doing mistake?
Please help!
 
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  • #2
90o is extreme. An interference pattern can be observed for n = 1 with small ##\theta##.

The problem is asking for an approximate answer. The general idea is that you need ##\lambda## to be "on the order of" the lattice spacing. So, what energy do you get if you take ##\lambda = 0.4## nm?
 
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  • #3
TSny said:
90o is extreme. An interference pattern can be observed for n = 1 with small ##\theta##.

The problem is asking for an approximate answer. The general idea is that you need ##\lambda## to be "on the order of" the lattice spacing. So, what energy do you get if you take ##\lambda = 0.4## nm?
p would get doubled and E would get 4 times, i.e., 4×2.35 eV = 9.4 eV ≈ 10 eV
 
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  • #4
Thank You so much for the help !
 
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FAQ: Electrons impinging on a crystal

1. What is the process of electrons impinging on a crystal?

Electrons impinging on a crystal refers to the phenomenon of electrons colliding with the atoms in a crystal lattice. This can happen in various ways, such as through scattering or diffraction, and can result in changes in the properties of the crystal.

2. How does the impinging of electrons affect the crystal structure?

The impinging of electrons can cause changes in the crystal structure, such as displacing atoms or creating defects. This is because the collisions between electrons and atoms can transfer energy, leading to vibrations and movements within the crystal lattice.

3. What are the applications of studying electrons impinging on a crystal?

Studying electrons impinging on a crystal can provide valuable insights into the behavior of materials at the atomic level. This knowledge can be applied in fields such as materials science, nanotechnology, and semiconductor technology.

4. How are electrons impinging on a crystal studied?

Electrons impinging on a crystal can be studied using various techniques, such as electron diffraction, scanning electron microscopy, and transmission electron microscopy. These techniques allow for the visualization and analysis of the interactions between electrons and the crystal lattice.

5. What are the potential challenges in studying electrons impinging on a crystal?

One challenge in studying electrons impinging on a crystal is the need for specialized equipment and techniques, which can be costly and require specialized training. Another challenge is the potential damage that can be caused to the crystal by the impinging electrons, which must be carefully controlled and monitored during experiments.

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