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Problem with units

by Henk
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Henk
#1
Oct14-05, 06:41 AM
P: 22
I'm having great difficulties with CGS-units. In an experiment involving NMR I have to calculate the proton-proton distance in CaSO4.2H2O.

I have done the measurements and they are, I think, pretty good however I have some problems with the calculations because of the units.

The formula I have to use is the following:

a = (3/2)(u*u0)/r^3

where u = 2.79*5.05*10^-27 J/T = 2.79*5.05*10^-24 erg/Gauss and u0 is the Permeability of vacuum. a is something I measured and has a value of 4.5 Gauss.

I know that r should be about 1.5 Angstrom (spelling?). My instructor told me to use CGS-units (thus putting u0=1) but does that mean that the rest of the formula stays the same? Or are there other changes like an additional 4pi or something. If I just put u0=1 I get r = 1.67*10^-8 (but I don't know the units, I believe the CGS-unit for distance is cm in which case r=1.67*10^-10 m = 1.67 A which is pretty close to 1.5 A).
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vanesch
#2
Oct15-05, 04:02 AM
Emeritus
Sci Advisor
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P: 6,236
Quote Quote by Henk
I'm having great difficulties with CGS-units. In an experiment involving NMR I have to calculate the proton-proton distance in CaSO4.2H2O.
I have done the measurements and they are, I think, pretty good however I have some problems with the calculations because of the units.
The formula I have to use is the following:
a = (3/2)(u*u0)/r^3
where u = 2.79*5.05*10^-27 J/T = 2.79*5.05*10^-24 erg/Gauss and u0 is the Permeability of vacuum. a is something I measured and has a value of 4.5 Gauss.
I know that r should be about 1.5 Angstrom (spelling?). My instructor told me to use CGS-units (thus putting u0=1) but does that mean that the rest of the formula stays the same? Or are there other changes like an additional 4pi or something. If I just put u0=1 I get r = 1.67*10^-8 (but I don't know the units, I believe the CGS-unit for distance is cm in which case r=1.67*10^-10 m = 1.67 A which is pretty close to 1.5 A).
Why don't you do the calculations first in SI units, and convert in the end in CGS ? I also get confused often between CGS, Gaussian, Natural,... etc units concerning EM quantitities because indeed, some include a 4 pi, others don't etc...

So I then do everything in SI units, and fill in the 4 pi in the other units in order to obtain the same result


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