Nuclear magnetic field at the electron's average position in hydrogen's 21cm transition

[somebody-nobody]

Radio astronomers have found that besides its optical spectral lines,hydrogen exhibits a radio spectral line at a wavelength of 21cm.This spectral line arises from the interaction between magnetic moment of the electron and the magnetic moment of the nucleus.The electron is located within the magnetic field generated by the magnetic moment of the nucleus ,and when electron flips from the spin up to spin down orientation in this magnetic field ,it emits a photon at 21cm wavelength.

What is the value of the nuclear magnetic field at the average poston of the electron?


I don't understand what is meant by average position ,since there is only spin up or down .MAybe i am on wrong track!

 

[Meir Achuz]

They probably mean 0.529 Angstrom, the radius of the first Bohr orbit.
The electron position is described by a wave function that is spread out, but
its average distance is 0.529 Angstrom.

 

[somebody-nobody]

I still don't get it

I still dotn get it.

if hc/lambda=g(mi)B

where
g=gyromagnetic number
B=magnetic field

how do i get g and mi ?

 

[marcusl]

The 21cm line comes from the hyperfine (spin-spin) splitting. This link shows the full calculation
http://www.pha.jhu.edu/~rt19/hydro/hydro.html"
Formulas are included for the proton magnetic moment and field.