motivation: detailed spectra of stars differ from pure blackbodies:

Motivation:Detailed spectra of stars differ from pure blackbodies:

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)

The Balmer Lines

n = 1

n = 2

n = 4

n = 5n = 3

H H H

The only hydrogen lines in the visible wavelength range.

Transitions from 2nd to higher levels of hydrogen

2nd to 3rd level = H (Balmer alpha line)2nd to 4th 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 Orbitalsn = 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)

(ms = +/- ½)

(ml = -1, 0, 1) (ms = +/- ½)

(ml = -1, 0, 1) (ms = +/- ½)

(ml = -1, 0, 1) (ms = +/- ½)(ml = -2, -1, 0, 1, 2)

(ml = 0)

(ms = +/- ½)(ml = 0)

(ms = +/- ½)(ml = 0)

(ms = +/- ½)(ml = 0)

(ms = +/- ½)

(ml = -2, -1, 0, 1, 2) (ms = +/- ½)

(ml = -3, …, 3) (ms = +/- 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, ml, and ms)

Gradual Filling of n-Shells:

Russell-Saunders Coupling

l1

l3

l2

s1

s2

s3

e1

e3

e2

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:

EJ+1 – EJ = C(J+1)

S L J

0 1 10 2 2

0 3 3

1 1 0,1,2

1 2 1,2,3

1 3 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:

1.S = 0

2.L = 0, +1, -1

3.J = 0, +1, -1, but NOT J = 0 → J = 0

Terminology for Line Transitions1) Allowed transitions:

(b) Transition in singly ionized Oxygen: OII 4119 4P5/2 – 4D7/2

2p3s – 2p4p

Initial state Final state

Full shells / subshells left out: 1s2 2s2

Examples:

(a) Transition in neutral Carbon: CI 5380 1P1 – 1P0

Wavelength in Å

2p23p – 2p23d

Terminology for Line Transitions2) Forbidden transitions:

Transition in neutral Nitrogen: [NI] 5200 4S3/2 – 2D5/2

2p3 – 2p3

Transition in singly ionized Nitrogen: NII] 2143 3P2 – 5S2

2s22p2 – 2s2p3

3) Intercombination Lines:

Spectral Classification of Stars

Tem

pera

ture

Different types of stars show different characteristic sets of absorption lines.

Stellar spectra

OB

A

F

G

KM

Surface tem

perature

Spectral Classification of Stars

Mnemonics to remember the spectral sequence:

Oh Oh Only

Be Boy, Bad

A An Astronomers

Fine F Forget

Girl/Guy Grade Generally

Kiss Kills Known

Me Me Mnemonics

Hertzsprung-Russell Diagram

Temperature

Spectral type: O B A F G K M

Lum

inos

ityor

Abs

olut

e m

ag.

Morgan-Keenan Luminosity

ClassesIa Bright Supergiants

Ib Supergiants

II Bright Giants

III Giants

IV Subgiants

V Main-Sequence Stars

IaIb

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!