Putting it all together -or- How to build an atom

1. Putting it all together -or- How to build an atom

2. 4 quantum numbers needed to specify an electron's state The allowed energy levels are quantized much like or particle in a box. Since the energy level decreases a the square of n, these levels get closer together as n gets larger. There are a total of n subshells, each specified by an angular momentum quantum number , and having an angular momentum of

3. There are a total of orbitals within each subshell, these can be thought of as projections of the angular momentum on the z axis. The electron has an intrinsic magnetic moment called “spin”. The orientation of the angular momentum vector of this apparent rotation motion can only have a manitude of ½.

4. Putting the pieces together... z Moving charges give rise to magnetic fields, which will then interact. Since the magnetic moments never align with the “z-axis” the torque is never zero. y x

5. If the orbital angular momentum is zero, you have to think about how it interacts with the spin, as some magnetic potential energy will arise from that interaction.

6. Spectrosopic Notation

7. The Pauli Exclusion Principle The total wavefunction: must be antisymmetric for electrons!

8. Chemical properties of an atom are determined by the least tightly bound electrons. • Factors: • Occupancy of subshell • Energy separation between the subshell and the next higher subshell.

9. A pattern starts to emerge s shell l=0 Helium and Neon and Argon are inert…their outer subshell is closed. p shell l=1 Beryllium and magnesium not inert even though their outer subshell is closed…why?? Alright, what do we add next???

10. Uh-oh…3d doesn’t come next…why???

11. Charge screening orbiting electron “sees” net charge of +e…like hydrogen nucleus: charge +3e closed s “shell”: total charge -2e Note that for higher orbital angular momentum, the energy more nearly equals to the corresponding levels in hydrogen. The more nuclear charge an electron “sees”,

12. Influence of the radial wavefunction Note the “pulling down” of the energy of the low angular momentum states with respect to hydrogen due to the penetration of the electric shielding. 2s state more tightly bound since it has a nonzero probability density inside the 1s shell and “sees” more of the nuclear charge.

13. Sodium...not what we expect? Excited state 4s lies lower than 3d!! The energy separating shells becomes smaller with increasing n. Electrons in lower angular momentum states penetrate shielding more, and thus are more tightly bound. As the energy levels become closer together, some lower angular momentum states of higher n may actually have a lower energy.

14. Order of filling, then, is not what we naively expect. The degree of charge screening plays a BIG role.

16. Now we know where to put the transition metals 4s comes BEFORE 3d… …and apparently 5s comes before 4d, and 6s comes before 5d…

17. The term with the maximum multiplicity lies lowest in energy. Also, mutual repulsion forces electrons to higher energy states.

18. General order of filling shells Note the filling of aligned spins before “doubling up”.

19. Alright, so where on the periodic table do we make room for all of those f orbitals?? Lanthanide series (or “rare earths” due to low abundance) Actinide series Stick them at the bottom to keep things from getting too awkward.

21. Viola...the periodic table demystified

22. Putting the "periodic" in the periodic table The ionization energies are periodic… If you are filling shells in order of successively higher energies, why does this happen?? The atomic radius is surprisingly constant. Why does is not scale with the number of electrons?

23. n=1

24. n=2

25. n=3

26. X-ray spectra

27. Moseley's law

29. For a given multiplicity, the term with the largest value of L lies lowest in energy. electrons spend less time near each other, less coulomb repulsion. For atoms with less than half-filled shells, the level with the lowest value of J lies lowest in energy.