motivation:
DESCRIPTION
0. Motivation:. Detailed spectra of stars differ from pure blackbodies:. 0. 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 = 0.529 Å. E n = - Z 2 e 2 / (2 a 0 n 2 ). 0. The Balmer Lines. - PowerPoint PPT PresentationTRANSCRIPT
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!