Question

On atomic units:

We assume that the elementary charge, the reduced Planck constant, the Coulomb constant and the speed of light to be all equal to 1.

How come, then, the fine-structure constant becomes equal to 1/137 a.u.?

Answer 1

First the fine structure constant is a dimensionless quantity and has the same value in any system of units.

Obviously you cannot set all the factors equal to 1 for that would make a =1. You can set c, h/2pi and eo (permittivity of free space) =1 as do high energy physicists in a unit system referred to as natural units. But then the electron charge is re scaled to equal ~ 0.30282212.

Answer 2

Ah, right. So, what do you normalize to 1 to get a = 1/137? Do you keep c = 1? I mean, afterwards, if you want to express the speed of light in atomic units, it becomes 137 a.u.

Answer 3

The speed of anything is measured in displacement/time. meter/sec, miles/hour It turns out that alpha is unitless, a pure number.

Answer 4

Hm, there's something that I'm still missing. Say, in this lecture here they show the following:

http://www.phys.ufl.edu/~korytov/phz4390/note_01_NaturalUnits_SMsummary.pdf

"In Natural Units, the fine structure constant becomes \[\alpha = \frac{ e^2 }{ 4\pi } = \frac{ 1 }{ 137 }\]


Obviously, I can't substitute e with
\[1.6 * 10^{-19} C\]

Answer 5

Oh, I think I got it. I'm supposed to keep the value of the fine-structure constant as it is,
\[\alpha=7.3*10^{-3}\]
And only afterwards can I express the speed of light, keeping the elementary charge, the Coulomb constant and the reduced Planck constant equal to 1, so c = 137 a.u.

I hadn't realised that natural units and atomic units are different terms.

Answer 6

The term atomic unit is not a standard nomenclature that I am aware of. Atomic mass unit is. 1 amu is 1.6605.. x 10^27 kgms.

Answer 7

Well, we were speaking about atomic units in a class in computational chemistry. The professor showed us that you can express the speed of light as the reciprocal of the fine-structure constant. If you're a physicist, maybe your programme hasn't focused much on molecules. I've heard classes in physics talk mainly about atoms and subatomic particles.

Answer 8

I would be interested in seeing how that was done and knowing of what advantage it would be.

Answer 9

Skip that I found an article that explains the concept. You can set the mass of the electron, the charge of the electron, the reduced plank constant, and the Coulomb constant (permittivity of free space) equal to one thereby leaving the velocity of light equal to the reciprocal of the fine structure constant. All this to simplify the computations of equations so you don't have to carry a lot of constant around.

Answer 10

Yeah, that's it. Seems there are different systems of 'natural units'. I didn't know that there were Planck units, too. I guess scientists are just trying to simplify equations.