1. Chapter 10 Atomic Structure and Atomic Spectra

2. Objectives: Objectives: Apply quantum mechanics to describe electronic structure of atoms Apply quantum mechanics to describe electronic structure of atoms Obtain experimental information from atomic spectra Obtain experimental information from atomic spectra Set up Schrödinger equation and separate Set up Schrödinger equation and separate wavefunction into radial and angular parts Use hydrogenic atomic orbitals to describe Use hydrogenic atomic orbitals to describe structures of many-electron atoms Use term symbols to describe atomic spectra Use term symbols to describe atomic spectra

3. Fig 10.1 Emission spectrum of atomic hydrogen

4. Conservation of quantized energy when a photon is emitted.

5. n f = 1 n i = 2 n f = 1 n i = 3 n f = 2 n i = 3 Energy levels of the hydrogen atom where: Rydberg constant

7. Structure of Hydrogenic Atoms Schrödinger equation Separation of internal motion Separate motion of e - and nucleus from motion of atom as a whole

8. Coordinates for discussing separation of relative motion of two particles Center-of-mass meme mNmN

9. Schrödinger equation Separation of internal motion Separate motion of e - and n from motion of atom as a whole Use reduced mass, Result: where R(r) are the radial wavefunctions Structure of Hydrogenic Atoms

10. Fig 10.2 Effective potential energy of an electron in the H atom Shapes of radial wavefunctions dependent upon V eff V eff consists of coulombic and centrifugal terms: When l = 0, V eff is purely coulombic and attractive When l ≠ 0, the centrifugal term provides a positive repulsive contribution

11. Hydrogenic radial wavefunctions L n,l (p) is an associated Laguerre polynomial R = (N n,l ) (polynomial in r) (decaying exponential in r)

13. Fig 10.4 Radial wavefunctions of first few states of hydrogenic atoms, with atomic # Z

14. Interpretation of the Radial Wavefunction 1)The exponential ensures that R(r) → 0 at large r 2)The ρ l ensures that R(r) → 0 at the nucleus 3)The associated Laguerre polynomial oscillates from positive to negative and accounts for the radial nodes

16. 1s

17. 2s

18. 3s

19. 2p

20. 3d

22. Potential energy between an electron and proton in a hydrogen atom aoao +++--- One-electron wavefunction = an atomic orbital