Bohr Magneton Dimensional Units
Richard Saam
Quoting from a standard Physical Chemistry Text:
(Walter Moore, Third Edition page 565)
"The electron has an intrinsic angular momentum or
spin, which
gives rise to a corresponding magnetic moment. A
spinning electron may be
characterized like a little magnet with corresponding
magnetic moment
e h/(4 pi m c) or Bohr magneton (cgs system)
with a value of 9.27E-21 erg/gauss."
where
e = charge
h = Planck constant
m = electron mass
c = speed of light
It is interesting to note that dimensionally the units
(erg/gauss) are
equivalent to (gauss cm^3) where gauss is in cgs system
is dimensionally (g^1/2 cm^-1/2 sec^-1)
A logical deduction is that the Bohr magneton with
equivalent dimensional units (gauss cm^3) implies that
there is a volume component to the electron.
Is this in conformity with any experiment?
Richard Saam
John C. Polasek
wrote:
You might have gone through some unnecessary algebra. I have hte
expression eh/4pi*m, not eh/4pi*mc.
Your expression gives charge*meters sinc half your expression is the
Compton wave length.
Mr. Dual Space
(If you have something to say, write an equation.
If you have nothing to say, write an essay).
John Devers
>
> A logical deduction is that the Bohr magneton with
> equivalent dimensional units (gauss cm^3) implies that
> there is a volume component to the electron.
>
> Is this in conformity with any experiment?
>
> Richard Saam
What is the difference between the Bohr magneton and the magnon, can
you explain it in simpler terms than I have here?
I have read these quotes from somewhere.
Bohr magneton (N. Bohr) The quantum of magnetic moment.
Another type of quasi-particle is the magnon, which is particle which
propagates the motion of magnetic spin through a magnetic medium.
Particles are connected with a property of the ground state known as
broken symmetry this leads to new particles. Atoms can have magnetic
spin, at certain temperatures they are random at lower temps they
spontaineously align and their rotational symmetry breaks. This
breaking allows new disturbances in the solid these are recognised as
waves or particles. Rotational inertia prevents spins from responding
instantly, wave propogation occures when restoring forces encounter
inertia. Spin disturbances propagate as spin waves, or particles
called magnons.
and this combination and definition from here.
http://odessa.phy.sdsmt.edu/~sobolev/Home_pagefiles/brief-sum.htm
This field produces non-equilibrium magnon states at which the value
of the magnetic moment increases in comparison with the equilibrium
one at a given temperature.
In solid state physics, a magnon is the term for an elementary
excitation in which the direction of magnetization in a ferromagnetic
material, or that of a sublattice moment in an antiferromagnetic
material, is spatially nonuniform and propagates as a wave (spin
wave).
Also what is a magnon laser? I heard it generates coherent photons
from precessing electrons. Could you also have a magneton laser?
How do spinons and holons fit into all this with magnetons and
magnons?
What is a magnon spectrum? Could you have a magneton spectrum too? are
the magnetic moments variable in time?
eb...@lfa221051.richmond.edu
In article <2978f9d5.02100...@posting.google.com>,
John Devers <johnd...@froggy.com.au> wrote:
>What is the difference between the Bohr magneton and the magnon, can
>you explain it in simpler terms than I have here?
This is a bit like asking for the difference between an electron and
an election! They're completely different things that happen to have
similar names.
The Bohr magneton is a number; a magnon is a quasiparticle.
-Ted
--
[My posts come from a machine that doesn't accept incoming mail. To
e-mail me, use an address of the form user...@domain.edu, as opposed
to user...@machinename.domain.edu.]
Richard Saam
John Devers wrote:
[snip]
>
> What is a magnon spectrum?
see Kittel
antiferromagnet magnon spectrum
hbar omega =hbar omega(excitation) sin (k a)
ferromagnet magnon spectrum
hbar omega =4 J S (1 - cos(k a))
> Could you have a magneton spectrum too? are
> the magnetic moments variable in time?
In as much as variables? in
e h/(4 pi m c)
are variable in time
Richard Saam
John Devers
eb...@lfa221051.richmond.edu wrote in message news:<ansn0i$ec4$1...@lfa222122.richmond.edu>...
> The Bohr magneton is a number; a magnon is a quasiparticle.
>
> -Ted
Thanks Ted, I think I'm getting the idea now. I'll just check a bit,
if time and space were ever quantized could the Bohr magneton become a
quasi-particle?
Is the number just a measure of a moment in time? Could it ever be an
interaction exchange particle in it's own right?
eb...@lfa221051.richmond.edu
>eb...@lfa221051.richmond.edu wrote in message
news:<ansn0i$ec4$1...@lfa222122.richmond.edu>...
>> The Bohr magneton is a number; a magnon is a quasiparticle.
>Thanks Ted, I think I'm getting the idea now. I'll just check a bit,
>if time and space were ever quantized could the Bohr magneton become a
>quasi-particle?
I'm sorry, but I cant' ascribe any meaning to this at all. It
sounds to me exactly like the following:
If the Republicans retake control of the Senate, will the number 3
become a radish?
Numbers aren't particles, and particles aren't numbers. I have no idea
what it could mean to talk about the Bohr magneton (a number) becoming
a quasiparticle.
Sorry I can't be any more help to you; maybe someone else can.
John Devers
> Numbers aren't particles, and particles aren't numbers. I have no idea
> what it could mean to talk about the Bohr magneton (a number) becoming
> a quasiparticle.
Thanks again Ted, I hope someone can, isn't an electron just a number
in math? Take a 1022 MeV photon change it's momentum and you have aa
electon positron pair?
How does a torsor fit in with this idea? Can't you create a torsor in
time for the magnetic moment and call it a particle or am I getting
way off the track?
[Moderator's note: Quoted text deleted. I personally know of no sense
in which "an electron [is] just a number." -TB]
John Devers
Sorry I just remembered, the below are not quotes but my personal
summary of some research I did on the subject so it may not be exactly
right.
Any peer review appreciated:-)
Richard Saam
"John C. Polasek" wrote:
>
> You might have gone through some unnecessary algebra. I have hte
> expression eh/4pi*m, not eh/4pi*mc.
> Your expression gives charge*meters sinc half your expression is the
> Compton wave length.
But what is energy relationship in terms of observed electron energy
levels in a magnetic field?
>
>
> Mr. Dual Space
> (If you have something to say, write an equation.
> If you have nothing to say, write an essay).
As a reference
http://www.tcaep.co.uk/science/constant/detail/bohrmagneton.htm
note that Bohr Magneton is eh/4pi*mc
with numerical results as
energy/magnetic field
9.27400899(37)E-21 erg/gauss
9.27400899(37)E-24 joule/tesla
It would be my understanding that when a magnetic field is applied to an
electron, its energy level splits into energy levels in accordance with
eh/4pi*mc with quantized factor
sqrt(s(s+1)) where s = 1/2
The dimensionally the units
(erg/gauss) are
equivalent to (gauss cm^3) where gauss is in cgs system
is dimensionally (g^1/2 cm^-1/2 sec^-1)
A logical deduction is that the Bohr magneton with
equivalent dimensional units (gauss cm^3) implies that
there is a volume component to the electron within a magnetic field.
In other words, when one measures the energy level splits with an
electron in a magnetic field in terms of energy/magnetic field or
erg/gauss or joule/tesla, is one also measuring a volume effect on the
electron such that
magnetic field x volume = constant
= 9.27400899(37)E-21 gauss cm^3
= 9.27400899(37)E-24 tesla meter^3
and also quantized in terms of
sqrt(s(s+1)) where s = 1/2
Richard Saam
John C. Polasek
<rds...@att.net> wrote:
>"John C. Polasek" wrote:
>>
>> You might have gone through some unnecessary algebra. I have hte
>> expression eh/4pi*m, not eh/4pi*mc.
>> Your expression gives charge*meters sinc half your expression is the
>> Compton wave length.
SNIP
>As a reference
>
>http://www.tcaep.co.uk/science/constant/detail/bohrmagneton.htm
>
>note that Bohr Magneton is eh/4pi*mc
jp:
Check some other references. The mc in the denominator should be m. I
have seen that error too. Go Google Bohr Magneton and the 2d and 3d
items have mc, and they are wrong!
My original gripe still applies
>with numerical results as
>
>energy/magnetic field
>
>9.27400899(37)E-21 erg/gauss
>9.27400899(37)E-24 joule/tesla
jp:
These are correct results.
>It would be my understanding that when a magnetic field is applied to an
>electron, its energy level splits into energy levels in accordance with
>eh/4pi*mc with quantized factor
>
>sqrt(s(s+1)) where s = 1/2
>
>
>The dimensionally the units
>(erg/gauss) are
>equivalent to (gauss cm^3) where gauss is in cgs system
jp:
You're way off. If erg/gauss = gauss cm^3, then gauss =
sqrt(erg/cm^3), and it's far from being that.
[Moderator's note: In fact, Saam is right here. In the Gaussian
system, a gauss is dimensionally the same as sqrt(erg/cm^3). One way
to see this is to note that the energy density of the magnetic field
is B^2/8pi in Gaussian units, so a gauss^2 must be the same
dimensionally as an energy density.
If I'm not mistaken, the Bohr magneton is e hbar / 2 m in SI units
and is e hbar / 2 mc in Gaussian units.
Quoted text deleted. -TB]
Richard Saam
"John C. Polasek" wrote:SNIP
> >As a reference
> >
> >http://www.tcaep.co.uk/science/constant/detail/bohrmagneton.htm
> >
> >note that Bohr Magneton is eh/4pi*mc
>
>
> >with numerical results as
> >
> >energy/magnetic field
> >
> >9.27400899(37)E-21 erg/gauss
> >9.27400899(37)E-24 joule/tesla
>
> jp:
> These are correct results.
RDS:
and can be numerically calculated from e hbar / 2 mc
> >The dimensionally the units
> >(erg/gauss) are
> >equivalent to (gauss cm^3) where gauss is in cgs system
>
> jp:
> You're way off. If erg/gauss = gauss cm^3, then gauss =
> sqrt(erg/cm^3), and it's far from being that.
>
> [Moderator's note: In fact, Saam is right here. In the Gaussian
> system, a gauss is dimensionally the same as sqrt(erg/cm^3). One way
> to see this is to note that the energy density of the magnetic field
> is B^2/8pi in Gaussian units, so a gauss^2 must be the same
> dimensionally as an energy density.
>
> If I'm not mistaken, the Bohr magneton is e hbar / 2 m in SI units
> and is e hbar / 2 mc in Gaussian units.
All of which brings up the question:
Which expression is more related to reality
e hbar / 2 mc
or
e hbar / 2 m
In the early experimental history (1910 - 1920?)
of this phenomenon, the splitting
of atomic spectral lines was noted
when placed in magnetic field. Magnitude
of splitting (energy) was noted as
related to applied magnetic field or
in other words erg/gauss and equated to
e hbar / 2 mc =
9.27400899(37)E-21 erg/gauss
a grand synergy of theory and experiment.
Taking the c off as in
e hbar / 2 m
seems to depart from the experimental reality.
The c should be there.
Also Gaussian B^2/8pi or
energy density (erg/cm^3) seems to reflect reality
What is energy density in SI units?
Richard Saam
eb...@lfa221051.richmond.edu
In article <aop58v$irg$1...@lfa222122.richmond.edu>,
>> >9.27400899(37)E-24 joule/tesla
>>
>> jp:
>> These are correct results.
>
>RDS:
>and can be numerically calculated from e hbar / 2 mc
in Gaussian units, or e hbar / 2m in SI units. If you don't believe
me, try it!
SI: e=1.602e-19 C, hbar=1.055e-34 J s, m=9.109e-31 kg. Plug in the
numbers to find e hbar / 2m = 9.277e-24 J/T.
Gaussian: e=4.803e-10 statcoulombs, hbar=1.055e-27 erg s, m=9.109e-28
g, c=2.998e10 cm/s. Plug in the numbers to find e hbar / 2mc =
9.278e-21 erg/gauss.
There. You made me look up constants and get out my calculator.
I hope you're happy!
The moderator (who happens to be me) said
>> If I'm not mistaken, the Bohr magneton is e hbar / 2 m in SI units
>> and is e hbar / 2 mc in Gaussian units.
>
>All of which brings up the question:
>
>Which expression is more related to reality
>
>e hbar / 2 mc
>
>or
>
>e hbar / 2 m
This strikes me as an odd question. They're the same thing, just in
different units. They're equally "related to reality," just as 3.00e8
m/s and 186000 miles/s are equally "related to reality."
The difference here traces back to the definition of the magnetic
field. The Lorentz force due to a magnetic field is
F = q v x B
in SI units, and
F = q (v/c) x B
in Gaussian units. Which one is right? It's a matter of convention!
Worrying about which one is right is like worrying about whether the
name of the 13th element is "aluminum" or "aluminium."
Personally, I'll admit to a prejudice in favor of a system of units in
which E and B have the same dimensions, but that's a matter of
convention, convenience, and habit, not "physical reality."
>In the early experimental history (1910 - 1920?)
>of this phenomenon, the splitting
>of atomic spectral lines was noted
>when placed in magnetic field. Magnitude
>of splitting (energy) was noted as
>related to applied magnetic field or
>in other words erg/gauss and equated to
>
>e hbar / 2 mc =
>9.27400899(37)E-21 erg/gauss
I haven't read the original papers, so I don't know what system of
units they were using, but it wouldn't have changed things the least
bit if they'd measured the splitting in SI units (J/T), in which case
it would have been equal to e hbar / 2m, without the c.
>Also Gaussian B^2/8pi or
>energy density (erg/cm^3) seems to reflect reality
Hmm. Go talk to a diehard Heaviside-Lorentz fan some time, and
they'll tell you just as fervently that an energy density of B^2 / 2
"reflects reality." Again, it's just convention!
>What is energy density in SI units?
Well, I already had to dig out my copy of Jackson to find out the
electron charge in statcoulombs, so I can look this up easily enough.
Let's see, according to Jackson's fabulously useful appendix on units,
you can turn a Gaussian B into an SI B*sqrt(4pi/mu0), so I guess the
answer is
B^2 / 2mu0.
Now that I look at that, it does seem familiar.