magnetic moment of electron

[granpa]

spin of electron=s=1/2

S=(h/2π)*√s(s+1)

μ_s=S*g_s*q/2m

g_s=2

 

l=0 or 1 or 2 ... up to n-1

L=(h/2π)*√l(l+1)

μ_L=L*g_L*q/2m

g_L=1

 

net magnetic moment of electron in subshell l = μ_s + μ_L

 

is this correct?

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also do the 2 components have the same sign? is the sum greater than or less than the magnetic moment due to spin alone?

[swansont]

Looks right. You can double-check

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

 

The sum depends on the spin orientation and projection of the orbital term— there are rules for adding angular momentum vectors, but this is simplified by having only a spin-1/2 particle involved

 

http://en.wikipedia.org/wiki/Angular_momentum#Addition_of_quantized_angular_momenta

 

So you'll have L +/- 1/2 states, e.g. an electron in an L=1 state is going to have either J=1/2 or 3/2

[granpa]

that website has changed since I took my notes. it hasnt become any clearer.

 

so if we restrict ourselves to talking about the component of magnetic moment in any one direction (the z direction) then the math becomes very much simpler.

 

μ_B=the bohr magneton (a unit magnetic moment)

 

for spin:

μ_z=-g_sμ_Bm_s

g_s≅2

m_s=1/2

 

for orbital magnetic moment:

μ_z=-g_Lμ_Bm_L

g_L=1

m_L=l,l-1,...,-l

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here is an excellent article on the magnetic moment of electrons:

http://www.shef.ac.uk/physics/teaching/phy332/atomic_physics6.pdf

[Severian]

It is only approximately right. g_s isn't exactly 2.

[granpa]

that website has changed since I took my notes. it hasnt become any clearer.

 

so if we restrict ourselves to talking about the component of magnetic moment in any one direction (the z direction) then the math becomes very much simpler.

 

μ_B=the bohr magneton (a unit magnetic moment)

 

for spin:

μ_z=-g_sμ_Bm_s

g_s≅2

m_s=1/2

 

for orbital magnetic moment:

μ_z=-g_Lμ_Bm_L

g_L=1

m_L=l,l-1,...,-l

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here is an excellent article on the magnetic moment of electrons:

http://www.shef.ac.uk/physics/teaching/phy332/atomic_physics6.pdf

 

yet m_j=m_l+m_s

 

not m_j=m_l+2*m_s even though g_s≅2