quizzicalteenager wrote:I think the answer to this question needs some help from Knight. I believe that scientists have come up with an approximate measure for the diameter of an electron. If you were to find this measure, should it exist, and convert it, I am sure that you can come up with an actual approximate answer to this question (yes, an actual approximate answer... the size of an electron, at least to my knowledge, is not scientifically proven, but merely guessed at).
According to The World Book Encyclopedia "The diameter of an electron is less than 1/1000 the diameter of a proton. A proton has a diameter of approximately 1/25,000,000,000,000 inch (0.000000000001 mm)." (
World Book Encyclopedia. Chicago: World Book) That would place the size of an electron at < 10^-18 m. According to Linus Pauling, "The radius of the electron has not been determined exactly but it is known to be less than 1 x 10-13 cm" (Pauling, Linus.
College Chemistry. San Francisco: Freeman, 1964: 57, 4-5.) That would give us a value of < 10^-15 m.
Trying to determine the size of an electron runs us into an old nemesis, the uncertainty principle. The short version is that we can know the location of an object, or we can know its speed. Not both. Since the bloody things move around so much, we can’t get a good look at them to figure out their shoe size.
However, we can take a round-a-bout way to figure out the radius: The Classical Electron Radius, or the Compton radius, is defined by equating the electrostatic potential energy of a sphere of charge e and radius Ro with the rest energy of the electron:
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e²
U = ---- = MeC²
Ro
where -e is the charge on the electron, Me is the electron mass, and c is the speed of light. Solving for Ro yields:
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e²
Ro = -----
MeC²
NIST defines the Classical Electron Radius as 2.817940285 × 10-15 m.
However, according to Malcolm H. Mac Gregor, “The electron is a point-like particle - that is, a particle with no measurable dimensions, at least within the limitations of present-day instrumentation. However, a rather compelling case can be made for an opposing viewpoint: namely, that the electron is in fact a large particle which contains an embedded point-like charge.” (Mac Gregor, Malcolm H.
The Enigmatic Electron. Boston: Klurer Academic, 1992: 4-5.)
There you have it. As clear and unfuddled as science can create. Now all you need to do is grab a bunch of electrons and convince them to line up, side by side. Just how many electrons are we going to need? Lets see:
If the minimum radius is 1e-18 m, then the diameter would be 2R, oe 2e-18 m.
therefore:
1e-09
------ = 5e8 electrons per micrometer.
2e-18
Assuming the maximum value of 1e-15 m. then we have a radius of 2e-15, giving us,
1e-09
----- = 5e5 electrons per micrometer
2e-15
So, were going to need somewhere between 500,000 and 500,000,000 electrons.
For your next assignment, I'd like you to take the average diameter of the head of a pin, in meters...
William J. Knight
Health Physicist
Los Alamos National Labs