Bohr Atom and the Fine Structure Constant (alpha)
alyosha in WV
alpha-squared (.000053248) times one-half the rest energy of the electron
(the latter is 510,999 eV). This produces a Bohr value of 13.605 eV for the
ground energy state of hydrogen. It is frequently said that this Bohr
ionization potential agrees with experiment, but actually, it doesn't. The
experimental value is about 13.598 eV
Is there an explanation for this discrepancy, or does one treat here of an
open question?
glird
By the numbers, 13.598/13.605 = .9994855. The minuscule discrepancy
is probably due to the word "about", in the experimental value.
Or it may be due to the fact that alpha-squared = .0000532513; from
which we get
.000053248/.0000532513 = .999938
as the discrepancy between the two different values of alpha^2.
(Btw, the internet value of alpha^2 is .007297352569^2 = .
00005325059. If we subtract my value of alpha^2 from that, and then
compare the result with that obtained by subtracting alyosha's, we get
a difference of .00000071 for mine and .0000259 for alnosir's; so al's
is 37 times worse than mine.)
glird
robert bristow-johnson
this may be non sequitur but a relationship between a_0 and alpha that
i think is interesting is
a_0/L_P = 1/[(m_e/m_P) * alpha]
where L_P and m_P are the Planck units and m_e is the electron mass.
we commonly say that "gravity is a weak force" because two electrons
(or two protons) alone in free space will interact negligibly
gravitationally compared to EM or other fundamental forces. but, in
Planck units, it's because the masses of particles are soooo much
smaller than the Planck mass, where the charge on the particles (if
they are charged) is in the same ballpark of each other. so saying
"m_e/m_P is small" is equivalent to saying "gravity is weak". but,
because alpha is not terribly big nor terribly small, then that is
saying the same as the Bohr radius is very large. but because 1/alpha
is a little bigger than one (2 orders of magnitude), the Bohr radius
is a little bit bigger than the electron mass is small.
but if you say this:
a_0/L_P = 1/(m_p/m_P) * (m_p/m_e)/alpha
where m_p (small p) is the proton mass. but then you're saying that
the Bohr radius is even more bigger than is the proton mass is small.
so the Bohr radius is a really big value because the particle masses
are really small values because, regarding fundamental forces, we
commonly think of gravity as really weak. it's all the same thing
(except for that factor of alpha).
that's my crankery.
r b-j
robert bristow-johnson
a sorta misnomer...
On Dec 18, 11:55�pm, robert bristow-johnson
<r...@audioimagination.com> wrote:
> this may be non sequitur but a relationship between a_0 and alpha that
> i think is interesting is
>
> � �a_0/L_P = 1/[(m_e/m_P) * alpha]
>
> where L_P and m_P are the Planck units and m_e is the electron mass.
>
> we commonly say that "gravity is a weak force" because two electrons
> (or two protons) alone in free space will interact negligibly
> gravitationally compared to EM or other fundamental forces. �but, in
> Planck units, it's because the masses of particles are soooo much
> smaller than the Planck mass, where the charge on the particles (if
> they are charged) is in the same ballpark of each other.
i meant to say that the charge of the particles (they're equal, of
course) are in the ballpark of the natural unit of charge, the Planck
charge (4*pi*eps_0*c*hbar)^(1/2). so they're about "normally"
charged, about 10^(-1), but way off-scale with respect to mass by
about 10^(-22). so the EM interaction will be about (10^21)^2 times
bigger in scale than the gravitational interaction.
> �so saying
> "m_e/m_P is small" is equivalent to saying "gravity is weak". �but,
> because alpha is not terribly big nor terribly small, then that is
> saying the same as the Bohr radius
... and the general size of atoms ...
> is very large. �but because 1/alpha
> is a little bigger than one (2 orders of magnitude), the Bohr radius
> is a little bit bigger than the electron mass is small.
>
> but if you say this:
>
> � �a_0/L_P = 1/(m_p/m_P) * (m_p/m_e)/alpha
>
> where m_p (small p) is the proton mass. �but then you're saying that
> the Bohr radius is even more bigger than is the proton mass is small.
>
> so the Bohr radius
... and the size of atoms ...
> is a really big value because the particle masses
> are really small values because, regarding fundamental forces, we
> commonly think of gravity as really weak. �it's all the same thing
> (except for that factor of alpha
... which is not so small nor large that it will change really
"big" things into small things or vise versa.
> that's my crankery.
... turn, turn, turn ...
r b-j