April 9

rest of term schedule

Mon               Thu
 9                11
16 (no class)     19  (chap 7 due)
23 (chap 8,9 due) 26 
30 (chap 10 due)

• (no class one week from today, April 16 - Jim is out of town)
• test 2 : on Apr 17 or 18, on chap 4,5,6
• test 3 : on Fri May 4, on chap 7, 8, 9, 10

The assignments for these aren't posted yet but will be soon.

We'll be doing 8 & 9 in a somewhat shallow fashion - look for the big picture ideas i.e. the periodic table.

You should read chapter 8 (many electron atoms) and 9 (molecules) - we'll be discussing that material Thursday & next Thursday..

review

• what are the n, l, m quantum numbers?
• what are orbitals (i.e. the pretty pictures we looked at last class)

answers

• n is energy (1/n^2) and radial quantum number
• l is length of orbital angular momentum quantum number
• m is z-component of orbital angular momentum quantum number
• the orbitals are eigenstate solutions of 3D schodinger equation for central 1/r potential

OK, on to the rest of chapter 7.

electron spin

continuing our discussion from last class ... one more quantum number : \( m_s \) = +1/2 or -1/2 for electron spin.

related wikipedia articles

• magnetic dipole
• Stern–Gerlach experiment - 1920ish silver atoms split into 2 spots ... evidence for spin 1/2 electrons
• Spin-1/2 (with a really cool animation of why 720 rotation is needed to return to "same"!)
• Spin–statistics theorem

energy levels

The angular momentum is labeled by letters :

l   0  1  2  3  4  5  ...
    s  p  d  f  g  h  ...

which gives us this notation :

4s (2 states)   4p (6 states)   4d (10 states)  4f (14 states)
3s (2 states)   3p (6 states)   3d (10 states)
2s (2 states)   2p (6 states)
1s (2 states)

Spectral line transitions : as an electron "falls" from (say) 3p (l=1) to 1s (l=0), it has a change angular momentum of \(\Delta l = 1\) . If it were to try to go from 3s to 1s, it would need to have \(\Delta l = 0\)

But photons have angular momentum of 1 !

• spin angular momentum of light

So the only transitions that happen have \(\Delta l = \pm 1 \)

splitting those degenerate levels

Zeeman effect

• apply an external magnetic field B
• change in energy levels is \( \Delta E = B \, \mu_B \, m_l \)
• so levels split proportional to B
• ... splits each \( m_l \) to different energy
• wikipedia

Fine structure

• electron in "orbit" around nucleus effectively sees nucleus orbiting around it
• ... and therefore experiences a magnetic field from interaction of L (orbital) and S (spin) rotation.
• ... splits each \( m_s \) to different energy
• ... but only about 1e-3 eV (compared to -13 eV ground state)
• wikipedia

hyperfine structure

• interaction between nucleus spin (magenetic moment) and electron spin (magnetic moment)
• even smaller, around 1e-6 eV
• most famous : 21 cm hydrogen line used in radio astronomy

up next : more than one electron

All of that is for one electron.

When we put more electrons around the nucleas, the same orbitals and shells and quantum numbers are useful abstractions, but the physics changes - each electron feels the effects of both the nucleus and the other electrons.

The biggest change is that the energy levels the electrons closer to the nucleas effectively shield the electric field from the electrons further out.

This means that the energy depends on radius in a new way, and in particular, the energy depends on both n and l in a non-trivial way.

The big result of the next chapter is the periodic table, which is a consequence of the pattern of how the electrons form "shells" with related quantum numbers, and therefore which electrons are most loosely bound and available to interact with those in other atoms.