De Broglie wavelength computable by just fixing speed of light ?

[xortdsc]

Hi,

I was wondering if it is possible to compute e.g. bohr radii for a metric system whose correspondence to real units is unknown and only the speed of light is known.

Let's say the only thing I know is that lightwaves travel x spaceunits in t timeunits, therefore defining the speed of light. The obvious problem is that I lack correspondance to real units such as meters for space and seconds for time.
So the question is: Is it possible to compute e.g. the bohr radius of an electron in groundstate in the hydrogen in units of x (or alternatively ct, lightspeed time) from just this defined lightspeed ? I've read that sometimes physisists set c=1 and hbar=1, but I don't get how to convert the dependent constants appropriately. Would this help solve my problem at all ? And if so how would this be done exactly ?

Thanks and cheers.

 

[xortdsc]

I think I figured it out finally. Turned out that system I meant was the Planck unit system. ;)

To compute the deBroglie wavelength of a 1s electron:

-> c                 = 1
-> h                 = 2pi
-> M (planck-mass)   = 2,1765e−8 kg
-> alpha             = 1/137
-> v                 = Z/n * alpha
-> v                 = 1/1 * 1/137
-> v                 = 1/137
-> m                 = m_e(in kg) / M
-> m                 = 9,10938291e-31 kg / 2,1765e−8 kg
-> m                 = 4,1853355892487939352170916609235e-23
-> lambda            = h / (m * v)
-> lambda            = 2pi / (4,1853355892487939352170916609235e-23 * 1/137)
-> lambda            = 20566962164152375997583578,037296

So this lambda-value can be interpreted as the distance a lightwave travels in 20566962164152375997583578 Planck-time units, right ?

so in meters this becomes

-> L (planck length) = 1,616199e−35 m
-> lambda_m (in m)   = lambda * L
-> lambda_m (in m)   = 20566962164152375997583578,037296 * 1,616199e−35 m
-> lambda_m (in m)   = 3,32403036827409059349185812403e-10 m

that seems fitting.

 

[xortdsc]

Well now that I have everything in Planck units I still don't see how that gives me result, because I don't know how many Planck time units my timeunit is. Don't I understand something here or is it really impossibe to compute because some necessary constant (t/T or x/L) is unknown ?