# Gyromagnetic ratio

1. Mar 15, 2014

### 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 μB (= 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:

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?

Last edited: Mar 15, 2014
2. Mar 15, 2014

### 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.

3. Mar 16, 2014

### bobie

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).

γe which is the ratio ofbetween the electron "spin" angular momentum Le= $\pm$1/2 h/2π = h/ 4π, and magnetic moment μe/Le
and ge, the g-factor , the experimental factor that multiplies the expected classical, theoretical value of ye 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?

Last edited: Mar 16, 2014