# Q & A: relativistic Doppler effect

Q:
I would like your take on several questions. 1) it is my understanding that the speed of the electron is approximately 20,000 mi./h. 2) I have been told that if a proton is the size of a baseball, and that baseball was put into San Francisco that the first electron orbit would be St. Louis Missouri. Trying to define the practical application of density versus size. 3) in the same vein of distance and orbits of the various electrons, what would be the distance between the rest of them right up to uranium 235? 4) if we had a space ship capable of C-1, and you held a flashlight let us say that frequency was 1000 cps if we were doing one half C-1 would be observable frequency be 500 cps? And if we were doing one half C-1 and we shot a beam of light from a flashlight from our spacecraft would are being light actually be doing 1.5 C-1? I have many more questions but I will wait to see if I have any answers. Thank you at least for the time you took to read this
- C Brooks (age old)
Anchorage,Ak.USA
A:

Let's start with the simple one, (4). The speed "c-1" doesn't actually mean anything, since "1" isn't a speed unless some units are given. Let's take 0.5c as a speed to illustrate what you're asking about. Say that the flashlight was blinking at your 1000 Hz, according to its own internal timer. How fast would it look like it was blinking to us as it approached us? It would be 1000Hz*sqrt((1+0.5)/(1-0.5))=1000Hz*sqrt(3) or ~1732 Hz. If it were going away from us the frequency would be 1000Hz/sqrt(3) = ~577 Hz. The speed of the beam of light would be exactly c according to us and according to the flashlight itself. Odd, but that's how the world is.

On (1), I guess you mean rough typical speeds in an atom. The most important thing to realize, however, is that the electron is not at any particular place and does not have any particular velocity. Both quantities are spread out. (See, e.g.  for a very extended discussion.)That doesn't mean that they're jumping between different values, they're just plain spread out. The spread is more like 2,000,000 mph in all directions for an electron in hydrogen.

On (2), the electron isn't at any particular distance. The electron spread on that scale (baseball-sized proton) would be about only be a few km, still in the Bay Area. For (3), in the bigger atoms it only goes up a little, because most of the electrons are squashed in more tightly around the nucleus.

Mike W.

(published on 11/30/2013)