4e Werkcollege SdM: Atoms and Molecules: 2009

4e Werkcollege SdM: Atoms and Molecules: 2009
Inleveren 23 Juni 2009 (PDF file)
Zeeman effect.
The Paschen α line in the hydrogen spectrum is due to the transition n=4 Æ n=3.
Sketch the Zeeman splitting for the 4p and 3d energy levels of the hydrogen atom,
and compute the magnitude of the splitting in a 2T applied magnetic field. Identify
all allowed 4p Æ 3d transitions and determine the shift from Paschen α for the
transition 4P3/2 (mj=-3/2) Æ 3D5/2(mj=-5/2). Hint include the Spin-orbit effect (but
you may ignore the relativistic effects); and calculate g-factors.
Consider a classical model of a spinning electron in terms of a uniformly dense
rotating sphere of mass me and radius re. Estimate re by identifying the rest energy
(mec2) with the electrostatic energy e 2 / 4πε 0 re . Obtain an expression for the
classical angular momentum and equate this quantity to h / 2 . Use the result to
solve for the speed v of an equatorial point on the surface of the rotating sphere, and
show that v is considerably larger than the speed of light.
Addition of angular momenta
Consider the NH molecule; this molecule is a radical, meaning it is an open shell
system. The electronic ground state is 3Σ-; so the relevant quantum numbers are
Λ=0, for the projection of the orbital angular momentum onto the internuclear axis
of the molecule (this means you may take L=0) and the spin S=1. The molecule
may rotate perpendicular to the internuclear axis with an angular momentum R. The
nuclear spin of the nitrogen nucleus (take 14N) is IN=1, and the nuclear spin of the
hydrogen nucleus is IH=1/2.
Add these angular momenta in the order N=L+R, J=N+S, F1=J+IN and F2=F1+IH.
Make a drawing of an energy level scheme for the NH molecule for N=1 and for
N=3 rotational states.