Double-slit experiment (electron gun directionality)

[lmerriam]

I'm having some trouble understanding why descriptions of the experiment (where single electrons are fired one after the other yet eventually forming an interference pattern) gloss over the issue of "how the electron gun is aimed" with respect to the barrier containing the two slits?

One, I presume, should imagine that the two-slit barrier is positioned directly in line with the electron gun: the individual electrons, therefore, being fired directly towards the barrier (more specifically, aimed perhaps to a point precisely between the two slits).

Imagined as a particle, no electrons could reach the screen to record the event -- each one would strike the barrier in the same spot between the slits, never passing through either one. Like bullets fired at a metal plate -- with two narrow slits a foot apart -- so long as the gun remains aimed directly between them, no bullets will ever get through.

If our electron gun, instead of being aimed towards the barrier, is aimed in the opposite direction .. obviously, no electrons will be recorded. But what if the electron gun was aimed sideways (i.e. 90-degrees to the apparatus)? What about 45-degrees, 25-degrees, and so on? At what point, will some electrons reach the screen to be recorded, and in what numbers (presumably having to do with the wavelength of the electron)?

I have no problem understanding that the spread out pattern of the electron strikes on the recording screen -- despite the gun being aimed directly between the slits -- is due to their wave nature. My confusion, however, is two-fold: (i) How, if at all, will this pattern vary when the gun is aimed obliquely to the apparatus (as noted above) and why?; and (ii) What factor(s) determine the overall size of the recorded points on the recording screen (i.e. the maximum height and width of the final 'image' on the screen)?

TIA!

 

[eljose79]

Hello, thank you for your question. The experiment you are referring to is known as the double-slit experiment and it is a classic demonstration of the wave-particle duality of matter. In this experiment, a beam of electrons is fired towards a barrier containing two narrow slits. On the other side of the barrier is a screen that records the pattern of the electrons that pass through the slits.

To answer your first question, the issue of how the electron gun is aimed is not typically glossed over in descriptions of the experiment. In fact, it is a crucial aspect of the experiment. The electron gun needs to be aligned with the barrier containing the slits in order for the electrons to pass through the slits and create an interference pattern. If the gun is not aimed directly at the slits, the electrons will not pass through them and no pattern will be observed on the screen.

To address your second question, the pattern on the screen does indeed vary depending on the angle at which the electron gun is aimed. If the gun is aimed obliquely, the pattern will be distorted and may not even appear as an interference pattern. This is because the angle at which the electrons are fired affects the distance they travel to the screen, causing the interference pattern to be shifted.

The overall size of the recorded points on the screen is determined by the wavelength of the electrons. The smaller the wavelength, the more closely packed the interference pattern will be on the screen. This is similar to how the size of the fringes in a double-slit experiment with light is determined by the wavelength of the light.

I hope this helps to clarify your understanding of the experiment. If you have any further questions, please don't hesitate to ask. Thank you for your interest in this fascinating topic!