Week 3: Light HW2 due on Thursday Read Ch. 5 (can skip 5.5) - - PowerPoint PPT Presentation

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Week 3: Light HW2 due on Thursday Read Ch. 5 (can skip 5.5) - - PowerPoint PPT Presentation

Feb 06, 2023 253 likes •516 views

Week 3: Light HW2 due on Thursday Read Ch. 5 (can skip 5.5) Galillama Galilei ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 1 Let there be LIGHT! Review of atomic structure, energy exchange processes, and spectroscopy

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ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Week 3: Light

1

HW2 due on Thursday Read Ch. 5 (can skip 5.5)

Galillama Galilei

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SLIDE 2

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Let there be LIGHT!

2

  • Review of atomic structure, energy

exchange processes, and spectroscopy

  • Radiative transfer
  • Thermodynamic equilibrium
  • Blackbody radiation
  • Wien’s Law
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SLIDE 3

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

“Light” is electromagnetic radiation of any wavelength/frequency, not just what eyes see

3

Classically, can be thought of a wave traveling down an electric field line like an induced transverse wave down a rope. In QM, quanta of the wave are called photons, which have energy and momenta determined by wavelength/frequency.

E = hν = hc λ h = 6.626 × 10−34 J s = 4.135 × 10−15 eV s c = 2.998 × 108 m s−1 ~ = h 2π

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1 eV = 1.602 × 10−19 J

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ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 4

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ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Atomic Structure (quantized energy levels)

5

mp = 1.673 × 10−27 kg

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me ≈ mp/1836 mn ∼ mp

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ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Atomic Structure (quantized energy levels)

6

Photon emitted with wavelength/ frequency equal to difference in energy between allowed

  • rbits (energy

levels)

En = −mec2 2 ↵2 Z n2 ↵ ≡ 1 4⇡✏0 e2 ~c ≈ 7.30 × 10−3 ≈ 1 137

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ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Energy Levels

7

∆E = En − En0 = (13.6 eV) Z2  1 (n0)2 − 1 n2

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(Energies correspond to neutral hydrogen)

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SLIDE 8

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Absorption of Energy

8

Photoexcitation Collisional Excitation

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SLIDE 9

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Absorption of Energy

9

Photoionization Collisional Ionization

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SLIDE 10

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Emission of Energy

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Spontaneous Emission Stimulated Emission Collisional De-excitation

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SLIDE 11

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Emission of Energy

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Radiative Recombination

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SLIDE 12

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Kirchoff’s Laws

12

  • A solid, liquid, or dense gas produces a continuous

spectrum.

  • A tenuous gas in front of a hot background produces

an absorption spectrum.

  • A tenuous gas in front of a cool background produces

an emission spectrum.

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ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 13

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ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 14

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ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Spectra are like Fingerprints

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They encode what and how much of an element is present in a gas (of a cloud, star, etc.), how hot it is, and whether it’s being excited by something else Each element has a unique pattern

  • f lines, which can be seen in

absorption or emission

∆E = En − En0 = (13.6 eV) Z2  1 (n0)2 − 1 n2

  • <latexit sha1_base64="bqw9mgF8fHl5v7Lg+vyS8IO63Cw=">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</latexit>
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ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 16

Stellar Types (different masses/temperatures)

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ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 17

“blueshifted” “redshifted” unshifted unshifted

z = ∆λ λ = ∆ν ν

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Allows us to infer motions along the “line of sight”

Doppler Shift

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ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Lines are not delta functions!

18

i.e., the difference b/t energy levels is NOT exact

Motion-induced Broadening (small Doppler shifts cause lines to appear more broad) Other Types of Broadening

  • Thermal Broadening
  • Rotational Broadening
  • Turbulent Broadening
  • Natural Broadening
  • Pressure Broadening
  • Zeeman Broadening

broadened

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SLIDE 19

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Natural Broadening

19

dNphot dt = n2A21

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A21 ∼ 108 s−1 ∼ 1 s−1

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(permitted) (forbidden) Heisenberg uncertainty principle

∆x · ∆p & ~

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(∆x c )(∆p · c) & ~ ∆t·∆E & ~

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ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Broadened Line Shapes

20

(ν − ν0)/σ

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Lorentzian Profile (natural broadening) Gaussian Profile (realistic broadening)

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SLIDE 21

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Lines are not delta functions!

21

i.e., the difference b/t energy levels is NOT exact

Other Types of Broadening

  • Natural Broadening
  • Pressure Broadening
  • Zeeman Broadening

broadened Dense environments, frequent collisions induce electric fields that modify energy levels

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SLIDE 22

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Doppler Broadening

22

Thermal Broadening

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SLIDE 23

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Velocity distribution of particles in thermal equilibrium have a Maxwell-Boltzmann distribution

23

F(v)dv = 4π ⇣ m 2πkT ⌘3/2 v2 exp ✓ −mv2 2kT ◆ dv

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F(E)dE = F(v) dv dE = 2 √πkT ✓ E kT ◆1/2 exp ✓ − E kT ◆

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hxi = Z xf(x)dx

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hvi = r 8kT πm

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hEi = 3 2kT

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  • Avg. particle speed
  • Avg. particle

kinetic energy

slide-24
SLIDE 24

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Doppler Broadening

24

Thermal Broadening line-of-sight “velocity dispersion” (width of a Gaussian distribution)

σlos = ✓ kT µmp ◆1/2 ≈ 100 m s−1 ✓ T 1 K ◆1/2 µ−1/2

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∆λ λ ≈ σlos c

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slide-25
SLIDE 25

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Lines are not delta functions!

25

i.e., the difference b/t energy levels is NOT exact

Motion-induced Broadening (small Doppler shifts cause lines to appear more broad)

  • Thermal Broadening
  • Rotational Broadening
  • Turbulent Broadening

broadened