Can you confirm the value of the g-factor for the spinning electron in H1?

[bobie]

I am studying the angular moment(s) in an atom of H (1s) in the classical model, can you help me understand some obscure points :
The mechanical orbital angular moment of the electron in 1s is L = mvr J*s:

(m) 9.11*10^-31 *(v) 2.1877*10⁶* (r) .52918*10^-10 = 1.0546*10^-34 J*s = h/2π,

the magnetic moment is μ = qvr/2 J/T:
1.6*10^-19*(v) 2.1877*10⁶* (r) .52918*10^-10 /2=9.274 *10^-24 J/T

first problem : this is the exact value of Bohr magneton μ_B (= qh/22πm), not of μ

The gyromagnetic factor γ (http://en.wikipedia.org/wiki/Magnetogyric_ratio) is the ratio μ / L : γ = qvr/2 *mvr = q/m2 (J/T / J*s =1/s*T) = 1.7588*10¹¹/2 radian/s*T, γ = 8.79*10¹⁰ r/Ts
For the spinning electron wiki says:

As mentioned above, in classical physics one would expect the g-factor to be g_e=1 ...(whereas it is 2.0023..., γ_e = 1.76*10¹¹: q/m 1.7588*g_e/2= 1.01169)

second question: how do I verify g=1, shall I take into account the electron classical radius 2.81*10^-15 m* 9.11*10^-31 kg and what speed?
Thanks for your help

 

[dauto]

What are you asking here? The definitions that you gave for L and μ are the classical definitions Using that definition the gyromagnetic ratio is just the charge to mass ratio (divided by 2). that relationship is not realized experimentally hence the need to define the g-factor that measures the discrepancy between the classical result and the observed value. The classical radius of the electron doesn't show up anywhere in either the classical or the quantum calculations.

 

[bobie]

What are you asking here?

hence the need to define the g-factor
The classical radius of the electron doesn't show up anywhere in either the classical or the quantum calculations.

In the article I quoted there is :
γ which is the ratio of the orbital momenta μ / L in H1 ( L = 1/2π and μ =q/2m).

γ_e which is the ratio ofbetween the electron "spin" angular momentum L_e= \pm1/2 h/2π = h/ 4π, and magnetic moment μ_e/L_e
and g_e, the g-factor , the experimental factor that multiplies the expected classical, theoretical value of y_e by 2.0023, if I got it right

The value of L in γ is mvr, where r should be the radius of the orbit in H1, Bohr radius
Isn't it so?