Nuclear Magnetic Field

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 dont understand what is meant by average position ,since there is only spin up or down .MAybe i am on wrong track!!

Meir Achuz

Science Advisor
Homework Helper
Gold Member
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 dont get it

I still dotn get it.

if hc/lambda=g(mi)B

g=gyromagnetic number
B=magnetic field

how do i get g and mi ?


Science Advisor
Gold Member
The 21cm line comes from the hyperfine (spin-spin) splitting. This link shows the full calculation" [Broken]
Formulas are included for the proton magnetic moment and field.
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