What is the significance of 54 volts in the Davidson Germer Experiment?

[Nikhil Rajagopalan]

In the experiment, a pronounced diffraction pattern is observed at an accelerating voltage of 54 volts. Beyond and below 54 volts, the peaks are not pronounced. What is the significance of 54 volts ? Why does the peak become less high below and above the specific value of accelerating voltage.

 

[vanhees71]

Do you have a source for this claim? Of course the voltage determines the electrons' momenta and thus their de Broglie wavelength. At a scattering angle determined by this wavelength you get the first maximum.

For a first explanation, see Wikipedia

https://en.wikipedia.org/wiki/Davisson–Germer_experiment

 

[Nikhil Rajagopalan]

The given scattering angle is 50 degrees and the selected accelerating voltage is 54 volts. If we are looking for the first maximum at a range exactly around 50 degrees of scattering angle, from the calculation, the accelerating voltage should be 54 volts. And beyond and below 54 volts, the first maximum may be displaced and the intensity diagram around 50 degrees of scattering angle will change. In that case, at a different accelerating voltage other than 54 volts, say 50 volts or 60 volts, there will still be a primary maxima observable but at a different angle of diffraction. Other than that, is there any other specific reason to choose 50 degrees and 54 volts as angle of scattering and accelerating potential respectively?

 

[gleem]

In the Wikipedia article, you should note that their original experiment did not agree with the Bragg equation. That is the measured peak did not occur at the angle which the Bragg equation predicted. The reason was that they failed to realize that the electrons have an index of refraction and are additionally redirected as they exit the crystal.

The following quote is taken from the paper of their continuing experiments.

FROM: REFLECTION OF ELECTRONS BY A CRYSTAL OF NICKEL
By C. J. DAVISSON AND L. H. Germer
BELL Telephone Laboratories Inc., New York City
Communicated March 10, 1928

https://www.pnas.org/content/pnas/14/4/317.full.pdf

"These results, including the failure of the data to satisfy the Bragg formula, are in accord with those previously obtained in our experiments on electron diffraction. The reflection data fail to satisfy the Bragg relation for the same reason that the electron diffraction beams fail to coincide with their Laue beam analogues. These differences between the electron and x-ray phenomena can perhaps be accounted for by assuming, as first suggested by Eckart,' that the crystal is characterized by an index of refraction for electrons as it is for x-rays, and that for electrons of the speeds used in our experiments the index has values which are quite different from unity.