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Natural Science Forum / Physics / Particle Physics / April 2008



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Experimentally Determined Rydberg Constant for Hydrogen

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Steve Bell - 20 Apr 2008 02:45 GMT
Does anyone know where I can find the value of an accurate, experimentally
determined Rydberg constant for hydrogen?

Thanks,
Steve Bell
Steve Bell - 20 Apr 2008 02:47 GMT
Since there is a one-to-one relationship between hydrogen's Rydberg constant
and its ground state binding energy, an accurate, experimentally determined
value of hydrogen's ground state binding energy would also be of interest to
me.

Steve Bell

> Does anyone know where I can find the value of an accurate, experimentally
> determined Rydberg constant for hydrogen?
>
> Thanks,
> Steve Bell
Tom Roberts - 20 Apr 2008 03:49 GMT
The Particle Data Group's "Particle Physics Booklet" gives a value
13.6056923(12) eV (the digits in parens are the uncertainty in the last
2 digits given). They usually give experimental references -- look in
http://pdg.lbl.gov

Tom Roberts

> Since there is a one-to-one relationship between hydrogen's Rydberg constant
> and its ground state binding energy, an accurate, experimentally determined
[quoted text clipped - 8 lines]
>> Thanks,
>> Steve Bell
Steve Bell - 20 Apr 2008 04:13 GMT
Hi Tom,

Thanks for the information. This value, when converted to a Rydberg
constant, looks like it gives R_inf. I'm looking for R_H, specifically an
accurate experimentally determined value for R_H. I don't think the
13.6056923 could be an true, "uncorrupted by theory" experimental value,
since an experimental value should show only real world effects, that is, it
should have "in it" the effect of finite nuclear mass. R_inf and its
associated binding energy does not, so it's difficult for me to accept the
13.6056923 value as truthfully what hydrogen itself "presents" to the
outside world.

Steve

> The Particle Data Group's "Particle Physics Booklet" gives a value
> 13.6056923(12) eV (the digits in parens are the uncertainty in the last
[quoted text clipped - 15 lines]
> >> Thanks,
> >> Steve Bell
Tom Roberts - 20 Apr 2008 15:56 GMT
> Thanks for the information. This value, when converted to a Rydberg
> constant, looks like it gives R_inf. I'm looking for R_H, specifically an
[quoted text clipped - 5 lines]
> 13.6056923 value as truthfully what hydrogen itself "presents" to the
> outside world.

The booklet calls this "Rydberg energy" and has a formula
h*c*R_\infinity = m_e*c^2*alpha^2/2. That clearly has nothing related to
the nucleus or proton in it, and it looks like a theoretical formula
based on experimental measurements of the constants involved rather than
direct measurements on hydrogen (though I believe those are involved in
measurements of \alpha). I am not familiar with the distinction you
make, I'm just reading the booklet and passing on its contents.

But look it up, as the PDG usually provides references for their data.

Tom Roberts

> Steve
>
[quoted text clipped - 21 lines]
>>>> Thanks,
>>>> Steve Bell
Steve Bell - 20 Apr 2008 16:42 GMT
Hi Tom,

The way the proton comes in, is to replace m_e, the rest mass of the
electron, with its reduced rest mass, which does involve the rest mass of
the proton. If that is done, values different than 13.5056923 eV and its
corresponding R_infinity are obtained. You have confirmed that the value
13.6056923 does not give R_H, but R_infinity. It sure looks hard to find an
accurate, "purely experimentally determined" (i.e., not derived by an
equation) Rydberg constant for hydrogen (R_H) on the net. I find that rather
surprising. The Wikipedia site presents a value:

http://en.wikipedia.org/wiki/Rydberg_constant

But it's from an equation. Perhaps there is no way to actually directly
measure either hydrogen's Rydberg constant or its ground state binding
energy. Once again, I would find that surprising. I tried looking at the
link you've given, but couldn't find the 13.6056923 number, but that is
exactly the number for R_infinity quoted at the above Wikipedia site. The
number 10967758.341 m^-1 is given for R_H. I wonder if physicists would say
that if indeed, R_H were determined directly from experimentation, this is
what would be obtained (with some slight difference, due to the particular
experimental error that occurred).

Thanks for the information,
Steve

> > Thanks for the information. This value, when converted to a Rydberg
> > constant, looks like it gives R_inf. I'm looking for R_H, specifically an
[quoted text clipped - 43 lines]
> >>>> Thanks,
> >>>> Steve Bell
Steve Bell - 20 Apr 2008 17:04 GMT
I've also found another link at:

http://www.lancs.ac.uk/users/spc/teaching/py301/phys301.htm

On page 9 of Part 5, a value of 1.0967759 x 10^-7 m^-1 is given, and it is
directly stated "from expt (line spectra)." This is real close to the
Wikipedia R_H value. I wonder if physicists would say, then, this is
actually the R_H value, and the corresponding binding energy is what
hydrogen itself physically binds the electron with in its ground state.

Steve

> Hi Tom,
>
[quoted text clipped - 72 lines]
> > >>>> Thanks,
> > >>>> Steve Bell
 
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