Role of accelerating voltage in Davisson Germer experiment

[Ahsan Khan]

Hello everyone,
We know Davisson & Germer experiment confirms the wave nature of electron(matter). Positions of Constructive Interference produces high intensity. So at different scattering angle intensity should be different. That's fine I understand why scattering angle(position) matters for position of maximum intensity as it happens at the position of Constructive Interference.

What I am not getting is why it needs a particular accelerating voltage for getting a peak of intensity they say Davisson and Germer find the intensity peak occurs at 54V and 50° scattering angle, and they go on to say that peak intensity at a particular angle shows Constructive Interference which is a characteristics of wave hence electrons are showing wave nature. I agree that the fact that scattered X-ray light(from Crystal)has Maxima at a particular angle makes it logical to consider electrons as wave but I am not getting here the role of accelerating voltage and why accelerating voltage affects position of maximum intensity and why accelerating voltage affect peak intensity. Below is a picture of intensity curves for different voltages at different angles.

Thanks a bunch.

 

[Doc Al]

I haven't looked at that work in detail, but realize that the electron wavelength depends on the energy. And when the wavelength is just right, the intensity is maximum.

 

[Keith_McClary]

The angle of the peak changes with the voltage, consistent with de Broglie scattering.

There is nothing special about 54V or 50 degrees, it's just that the peak was most conspicuous at that voltage.
Source.
(This looks like a schematic sketch, not actual data.)

 

[Ahsan Khan]

There is nothing special about 54V or 50 degrees, it's just that the peak was most conspicuous at that voltage.

Thanks Keith, I now understand that the location of peak is decide by the De Broglie wavelength of the incident electrons. However what I still fail to grasp is the reason why "the peak was most conspicuous at that voltage"(54V)?

Why the peak decreases after 54V of accelerating potential and how the accelerating potential affect the value of peak at the first place?

Regards

 

[Keith_McClary]

Thanks Keith, I now understand that the location of peak is decide by the De Broglie wavelength of the incident electrons. However what I still fail to grasp is the reason why "the peak was most conspicuous at that voltage"(54V)?

Why the peak decreases after 54V of accelerating potential and how the accelerating potential affect the value of peak at the first place?

Regards

You could look at their 1927 paper. In their Fig 10 there is little scattering near 90 degrees and a lot of background (noise?) at 0 degrees.

 

[Ahsan Khan]

You could look at their 1927 paper. In their Fig 10 there is little scattering near 90 degrees and a lot of background (noise?) at 0 degrees.

I looked at their paper, but some of the terms they are using are not known to me. I would be thankful to you if you help me understand the point being explained through figure 10(attaching figure below) which settles my curiosity of knowing the matter asked in the post.

Regards!

 

[Keith_McClary]

I looked at their paper, but some of the terms they are using are not known to me. I would be thankful to you if you help me understand the point being explained through figure 10(attaching figure below) which settles my curiosity of knowing the matter asked in the post.

Regards!

Disregard my above comments.
In Bragg scattering

you only get strong scattering for certain angles, depending on the spacing (and geometry) of the crystal lattice, AND only for certain wavelengths such that there is constructive interference from atoms in a three dimensional array. This is why they associate "beams" with a particular voltage (which determines the wavelength).

(The paper is a bit confusing because for "grazing" scattering they were getting diffraction from the two dimensional surface array of atoms (since the electrons did not penetrate into the crystal). This is discussed on p. 724.)

 

[Keith_McClary]

Correction: The angles depend only on the geometry, not the spacing. Constructive interference occurs when the ratio of the wavelength to the spacing has certain values.

 

[Ahsan Khan]

Correction: The angles depend only on the geometry, not the spacing. Constructive interference occurs when the ratio of the wavelength to the spacing has certain values.

I am getting what can be called "something close to explanation", a clarity could be attain if some data is employed and use maths in it to fully understand , why the peak is most conspicuous at 54V. Can this be shown?
Thanks for your continuous support.

Regards!

 

[Keith_McClary]

I am getting what can be called "something close to explanation", a clarity could be attain if some data is employed and use maths in it to fully understand , why the peak is most conspicuous at 54V. Can this be shown?
Thanks for your continuous support.

Regards!

What I said about "conspicuous" is wrong. Disregard.

According to the theory described in the Wikipedia article, you only get exact constructive interference when the path difference is precisely a multiple of the wavelength. This assumes an infinite crystal. In a crystal with only a few layers you will get nearly constructive interference over a range of wavelengths, so some diffraction is measured at voltages near 54V. In this experiment the electrons do not penetrate very far into the crystal, so only a few layers contribute.