Exploring the 21cm Radio Spectral Line of Hydrogen in the Nuclear Magnetic Field

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Radio astronomers have found that besides its optical spectral lines,hydrogen exhibits a radio spectral line at a wavelenght 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 wavelenght.

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!
 
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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.
 
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 ?
 
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.
 
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To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.
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