Motivation:

1. 0 Motivation: Detailed spectra of stars differ from pure blackbodies:

2. 0 The Bohr Model of the Hydrogen Atom Postulate: L = n ħ rn = a0 n2/Z Bohr radius: a0 = ħ2 / (mee2) = 5.29*10-9 cm = 0.529 Å En = - Z2e2 / (2 a0 n2)

3. 0 The Balmer Lines Transitions from 2nd to higher levels of hydrogen n = 1 n = 4 n = 5 n = 3 n = 2 Ha Hb Hg The only hydrogen lines in the visible wavelength range. 2nd to 3rd level = Ha (Balmer alpha line) 2nd to 4th level = Hb (Balmer beta line) …

4. 0 Hydrogen Line Series Infrared Optical Ultraviolet

5. 0 The Balmer Lines

6. 0 The Cocoon Nebula (dominated by Ha emission)

7. 0 The Fox Fur Nebula (dominated by Ha)

8. Possible Electron Orbitals n = 1 (K shell – 2 orbitals) (ml = 0) l = 0 (1s – 2 orbitals) (ms = +/- ½) n = 2 (L shell – 8 orbitals) (ml = 0) (ms = +/- ½) l = 0 (2s – 2 orbitals) (ml = -1, 0, 1) l = 1 (2p – 6 orbitals) (ms = +/- ½) n = 3 (M shell – 18 orbitals) l = 0 (3s – 2 orbitals) (ml = 0) (ms = +/- ½) l = 1 (3p – 6 orbitals) (ml = -1, 0, 1) (ms = +/- ½) (ml = -2, -1, 0, 1, 2) (ms = +/- ½) l = 2 (3d – 10 orbitals) n = 4 (N shell – 18 orbitals) (ml = 0) l = 0 (4s – 2 orbitals) (ms = +/- ½) (ml = -1, 0, 1) (ms = +/- ½) l = 1 (4p – 6 orbitals) l = 2 (4d – 10 orbitals) (ml = -2, -1, 0, 1, 2) (ms = +/- ½) l = 3 (4f – 14 orbitals) (ml = -3, …, 3) (ms = +/- ½)

9. 0 Quantum-Mechanical Localization Probability Distributions

10. 0 Energy Splitting Beyond Principal Quantum Number B m

11. 0 The Pauli Principle No 2 electrons can occupy identical states (i.e., have the same n, l, ml, and ms)

12. 0 Gradual Filling of n-Shells:

13. 0

14. 0 Filled shells: L = S = J = 0 e2 e1 Russell-Saunders Coupling e3 l1 s1 L l2 s2 J l3 s3 S

15. 0 Atomic Energy Levels S L J 0 1 1 0 2 2 0 3 3 1 1 0,1,2 1 2 1,2,3 1 3 2,3,4 Hund’s Rule 2: For given S, states with larger L have lower energies Hund’s Rule 1: States with larger S have lower energies Lande’s Interval Rule: EJ+1 – EJ = C(J+1)

16. Electric Dipole Transition Selection Rules Radiative transitions are most likely for electric dipole (E1) transitions. Possible if the following Selection Rules are obeyed: • DS = 0 • DL = 0, +1, -1 • DJ = 0, +1, -1, but NOT J = 0 → J = 0

17. Terminology for Line Transitions 1) Allowed transitions: Examples: (a) Transition in neutral Carbon: CIl5380 1P1 – 1P0 Final state Initial state 2p3s – 2p4p Wavelength in Å Full shells / subshells left out: 1s2 2s2 (b) Transition in singly ionized Oxygen: OIIl4119 4P5/2 – 4D7/2 2p23p – 2p23d

18. Terminology for Line Transitions 2) Forbidden transitions: Transition in neutral Nitrogen: [NI] l5200 4S3/2 – 2D5/2 2p3 – 2p3 3) Intercombination Lines: Transition in singly ionized Nitrogen: NII] l2143 3P2 – 5S2 2s22p2 – 2s2p3

19. 0 Spectral Classification of Stars Different types of stars show different characteristic sets of absorption lines. Temperature

20. 0 Stellar spectra O B A F Surface temperature G K M

21. 0 Spectral Classification of Stars Mnemonics to remember the spectral sequence:

22. 0 Hertzsprung-Russell Diagram Absolute mag. Luminosity or Temperature Spectral type: O B A F G K M

23. 0 Morgan-Keenan Luminosity Classes Ia Bright Supergiants Ia Ib Ib Supergiants II III II Bright Giants III Giants IV V IV Subgiants V Main-Sequence Stars

24. 0 The Balmer Thermometer Fraction of neutral H atoms in the excited (n = 2) state (Boltzmann Equation) Number of neutral H atoms in the excited (n = 2) state available to produce Balmer lines Fraction of ionized Hydrogen atoms (Saha Equation)

25. 0 Measuring the Temperatures of Stars Comparing line strengths, we can measure a star’s surface temperature!