# Homework Help: Fine structure of sodium spectrum

1. Mar 22, 2007

### Amith2006

1. The problem statement, all variables and given/known data
Estimate the strength of magnetic field produced by the electron’s orbital motion which results in the 2 sodium lines(5890 & 5896 Angstrom).

2. Relevant equations

3. The attempt at a solution

Let E be the potential energy of a magnetic dipole when placed in an external magnetic field B, M(z) be the component of magnetic dipole moment vector along the direction of B, m(s) be the magnetic spin quantum number, S be the spin angular momentum, l be the orbital quantum number
This transition occurs between an l=1 state and an l=0 state. Only the l=1 state is split. The difference in energy between the l=1 sub states can be obtained from the wavelength difference.
E =hc/(lambda)
dE = [hc/( lambda)^2]|d(lambda)|
= 2.13 X 10^(-3) eV
This energy can be related to the magnetic field produced by the electron’s orbital motion.
E = -M(z)B
= (e/m)[m(s)][h/2(pi)]B
Differentiating the above equation we get,
dE = (e/m)[d(m(s))][h/2(pi)]B
i.e. 2.13 X 10^(-3) = (e/m)[d(m(s))][h/2(pi)]B
In the next step they have found B by taking d(m(s))= [1/2 –(-1/2)]=1
This is possible if the electrons in one sub state have m(s)=+1/2 and in another sub state they have m(s)= -1/2
Does this mean that the electrons in the 2 sub states are having opposite spins?