Atomic structure

1. Atomic structure 3.1. Structure and spectra of hydrogenic atoms 3.1.1 The structure of hydrogenic atoms 3.1.2 Atomic orbitals and their energies 3.1.3 Spectroscopic transitions and selection rules 3.2. The structure of many electron atoms 3.2.1 The orbital approximation 3.2.2 The spectra of complex atoms 3.2.3 Singlet and triplet states 3.2.4 Spin-orbit coupling

2. Spherical coordinates 1 x = r sin cos y = rsin sin z = r cos

3. Radial 1

4. Radial 2

5. Average distance Spherical coordinates For a given n, the mean radius follows the order d < p < s

6. p-orbitals 1

7. p-orbitals-2 pz py Y(θφ) px R(r)Y(θφ)

8. d-orbitals In the shell n=3, there are 3 subshells:  l= 0  ml= 0  1 s-orbital  l= 1  ml= -1, 0, 1  3 p-orbitals  l= 2  ml= -2, -1, 0, 1, 2  5 d-orbitals From a linear combination of these orbitals, we can build real orbitals that are also solutions of the SE for the hydrogenic atom: dxy, dyz, dzx, dx2-y2, dz2

9. 2s 1s Effective charge

10. Ordering of orbitals as f. of Z

11. Electron configurations Pauli exclusion principle: “No more than 2 electrons may occupy any given orbital. If 2 electrons occupy one orbital, then their spin must be paired (antiparallel: ).” Hund’s rule: “An atom in its ground state adopts a configuration with the greatest number of unpaired electrons”

12. Spin correlation • two electrons with different spin (antiparallel) have • a certain probability to be at the same position. • The electrostatic repulsion is increased:the system in itssinglet state is destabilized • when 2 electrons in 2 different orbitals have the • same spin(parallel), they are repelled to each other • thanks to their spin. • that prevents an additional electrostatic repulsion. The Triplet state (2 spins parallel) is more stable than the singlet state (2 spins antiparallel) this is the explanation for Hund’s rule.

13. He-atom l= 1, ml = 0, 1

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