# Questions on Paschen's Law and Photoelectron Behaviors

1. Apr 1, 2014

### AutoNub

Hello Gentlemen,

I'm fairly new to the quantum physics side of electromagnetic and atomic theory, so please be gentle. I'm interested in the antenna broadcasting application and I'm working on developing a clearer understanding of exactly what occurs on an atomic level when an antenna broadcasts.

Based on my interpretation of my recent research, it appears photons collide with free electrons on the antenna surface and photo electrons (low energy phenomena) are ejected (depending on the photon collision energy versus the bonding energy of the pairing ions). I understand this electromagnetic behavior can be expressed by drawing or visualizing an oscillating wave pattern, where the magnetic field polarity changes once per wave cycle, and the photo electron polarity also changes, at a right angle to the magnetic field polarity, once per wave cycle (these directions are commonly expressed using Fleming's left-hand rule). So if we imagine a series of alternating vertically oriented arrows with alternating plus and minus signs to the right of each arrow, where the arrows indicate the vertical (y-coordinate) direction of the photo electron flow and the + or - signs indicate the outward or inward (z-coordinate) direction of the magnetic field, we can see the electromagnetic field behavior as it propagates outward.

The acceleration due to the changing magnetic field and electron flow on the surface of the antenna is what enables these collisions to take place with sufficient energy (a combination of kinetic and electric) for the photo electrons to break free of the antenna surface and radiate outward in all directions opposite to the conductor source. These electromagnetic fields radiated outward lose kinetic energy as a function of frequency and distance. The higher the frequency, the faster the photo electron spin and oscillation and thus the greater the friction through the medium (typically air), which means higher frequency signals have reduced range. The lower the frequency, the slower the photo electron spin and oscillation and thus the lower the friction through the medium, which means lower frequency signals have an increased range. This explains why, for example, AM (535-1705 kHz) radio stations generally have greater range than FM (88-108 MHz) stations. Since the higher frequencies have shorter wavelengths (lambda = c/f), the FM station is generally higher quality due to more information being transferred in the same amount of time compared to lower frequencies.

There is a limit for the amount of power you can send to an antenna and this limit is dictated by the dielectric breakdown voltage and the ampacity. Paschen's Law describes the theory and how the calculation can be performed. It is described by the equation V=[(a*p*d)/(ln(p*d)+b)], where V is the breakdown voltage. Referring to Wikipedia for more detail, we can calculate the voltage necessary to cause an arc (i.e., dielectric breakdown) between two antenna elements using the aforementioned equation. However, at the bottom of the Wikipedia article, in the conclusions and validity section, it says "the creation of further free electrons is only achieved by impact ionization. Thus Paschen's law is not valid if there are external electron sources. This can for example be a light source creating secondary electrons via the photoelectric effect. This has to be considered in experiments." Based on this statement, isn't the example it offers where air is the medium between the conductors invalid? Air is a gas which has mass, and since it isn't made up of pure hydrogen, it has valence electrons which can behave as free electrons. Thus, air is an "external electron" source. So is Paschen's Law and the given formula valid for antenna elements in an air medium or not?

I understand broadcast range is increased in a vacuum due to the absence of a friction causing medium, but what about in a vacuum amidst perfect darkness without the presence of an external photon source? Are photo electrons created by the collisions between ions through the antenna conductor? If this is the case, would it be fair to state that the number of photo electrons transmitted from the antenna would be fewer in number?

Is my interpretation on antenna radiation and broadcasting correct? If not, please correct me and please also elaborate on any details I may have missed. Don't be afraid to give too much detail, but please don't simply refer me to a text book either.

On a more fundamental level, if a radio is tuned to receive a specific frequency (i.e, 104.7 MHz), then how does the information get picked up from the radio signal (the photo electron collisions on the receiving antenna) if the information is, by definition, transmitted via frequency modulation? In other words, if the receiver is tuned to receive 104.7, and the transmitter is modulating the frequency (i.e., encoding the information) around 104.7, then wouldn't the frequency modulation change the frequency to some frequency other than 104.7? In other words, if the frequency is constantly changing as a function of the encoded information being transmitted, then how does the receiving antenna decode it when it is only tuned to receive 104.7? What about station 104.9? Or does the modulation occur within a specific range which might explain the (arbitrarily selected as an example) unused frequencies between 104.7 and 104.9 (a difference of 0.2 MHz)? If this is the case, would it be safe to assume (f2-f1)/2 is the allotted modulation range (bandwidth) for each FCC approved station?

Thanks in advance for the clarifications!

Last edited: Apr 1, 2014