Motivation: Detailed spectra of stars differ from pure blackbodies:

The Bohr Model of the Hydrogen Atom Postulate: L = n ħ r n = a 0 n 2 /Z Bohr radius: a 0 = ħ 2 / (m e e 2 ) = 5.29*10 -9 cm = Å E n = - Z 2 e 2 / (2 a 0 n 2 )

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

Hydrogen Line Series Ultraviolet Optical Infrared

The Balmer Lines

The Cocoon Nebula (dominated by H  emission)

The Fox Fur Nebula (dominated by H  )

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

Quantum-Mechanical Localization Probability Distributions

Energy Splitting Beyond Principal Quantum Number m B

The Pauli Principle No 2 electrons can occupy identical states (i.e., have the same n, l, m l, and m s )

Gradual Filling of n-Shells:

Russell-Saunders Coupling l1l1 l3l3 l2l2 s1s1 s2s2 s3s3 e1e1 e3e3 e2e2 L S J Filled shells: L = S = J = 0

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

Electric Dipole Transition Selection Rules Radiative transitions are most likely for electric dipole (E1) transitions. Possible if the following Selection Rules are obeyed:  S = 0  L = 0, +1, -1  J = 0, +1, -1, but NOT J = 0 → J = 0

Terminology for Line Transitions 1) Allowed transitions: (b) Transition in singly ionized Oxygen: O II P 5/2 – 4 D 7/2 2p3s – 2p4p Initial stateFinal state Full shells / subshells left out: 1s 2 2s 2 Examples: (a) Transition in neutral Carbon: C I P 1 – 1 P 0 Wavelength in Å 2p 2 3p – 2p 2 3d

Terminology for Line Transitions 2) Forbidden transitions: Transition in neutral Nitrogen: [N I ] S 3/2 – 2 D 5/2 2p 3 – 2p 3 Transition in singly ionized Nitrogen: N II ] P 2 – 5 S 2 2s 2 2p 2 – 2s2p 3 3) Intercombination Lines:

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

Stellar spectra O B A F G K M Surface temperature

Spectral Classification of Stars Mnemonics to remember the spectral sequence: OhOhOhOhOnly BeBeBoy,Bad AAnAnAstronomers FineFForget Girl/GuyGradeGenerally KissKillsKnown MeMeMeMeMnemonics

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

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

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

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