Today: Chapter 5 - uwyo.edu

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Astr 1050 Mon. Sept. 23, 2015

Today: Chapter 5 – Light: The Cosmic Messenger

Wed: Begin Ch. 6

Reading: For Wednesday: Chapter 6

Homework #5 due Monday March, 2 Homework #6 due Friday March, 6

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Some Good Star Quotes

•  “Be humble, for the worst thing in the world is of the same stuff as you; be confident, for the stars are of the same stuff as you.” –Nicholai Velimirovic

•  “No pessimist ever discovered the secrets of the stars or sailed to an uncharted land or opened a new heaven to the human spirit.” - Helen Keller

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Atoms – Historical Development •  To some Greeks, were smallest “indivisible” unit of matter

•  In 1700’s, 1800’s discovery of chemical “elements” (H, He, C, O, N, ...)

somehow made of different kinds of atoms

•  In early 1900’s, parts of atoms and reasons the elements differ understood

•  In early to mid 1900’s ways to change one kind of atom into another understood –  radioactive decay –  fission –  fusion

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Atoms – Basic Characteristics •  Very small (for 1H: mass = 1.67×10-27 kg Diameter = 0.4 nm = 4×10-10 m)

•  Composed of an even smaller nucleus and an “orbiting” cloud of electrons –  Nucleus is very small even compared to size of atom (for 1H: D=1.6 ×10-15 m)

•  So atoms are mostly empty space –  Nucleus contains almost all the mass and is positively charged –  Electrons are negatively charged and usually balance charge of nucleus

•  Almost like a miniature solar system: Sun ⇒ Nucleus, Planets ⇒ Electrons –  Like solar system, atoms are mostly empty space (nucleus small) –  Like solar system, force is 1/r2, but from electric attraction, not gravity –  Unlike solar system, need to use Quantum Mechanics, not Newtonian Mechanics

•  Only certain Electron “Orbits” will be allowed by Q.M.

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Atoms – Constituent Parts I

•  Atoms contain 3 kinds of particles: – Electrons – in orbits Negatively charged

Very low mass (1/1836 mp) – Protons -- in nucleus Positively charged

More “massive” – Neutrons – in nucleus Electrically neutral

mn ≈ mp

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Atoms – Constituent Parts II

•  # of protons (Z) determines charge of nucleus ⇒ electrical properties ⇒ element –  Chemical reactions involve sharing/exchanging

electrons (See periodic table A-16) –  Hydrogen: Z=1 –  Helium: Z=2 –  Lithium: Z=3 –  Carbon: Z=6

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Atoms – Constituent Parts III

•  # of protons and # of neutrons determines mass and nuclear properties –  Same element (same Z) but different # of neutrons ⇒

isotope of same element –  Isotopes behave same chemically, but have different

nuclear properties –  1H = 1 proton, 0 neutrons (regular hydrogen) –  2H = 1 proton, 1 neutron (deuterium) –  3H = 1 proton, 2 neutrons (tritium) –  4He= 2 protons, 2 neutrons (regular helium)

–  12C = 6 protons, 6 neutrons (regular carbon) 14C = ???

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Atoms – Electron Configuration

•  Molecules: Multiple atoms sharing/exchanging electrons (H2O, CH4)

•  Ions: Single atoms where one or more electrons have escaped (H+)

•  Binding energy: Energy needed to let electron escape

•  Permitted “orbits” or energy levels –  By rules of quantum mechanics, only certain “orbits” are allowed –  Ground State: Atom with electron in lowest energy orbit –  Excited State: Atom with at least one atom in a higher energy orbit –  Transition: As electron jumps from one energy level orbit to another,

atom must release/absorb energy different, usually in form of light.

•  Because only certain orbits are allowed, only certain energy jumps are allowed, and atoms can absorb or emit only certain energies (wavelengths) of light.

•  In complicated molecules or “solids” many orbits and transitions are allowed

•  Can use energy levels to “fingerprint” elements and estimate temperatures.

From our text: Horizons, by Seeds

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Temperature and Heat

•  Thermal energy is “kinetic energy” of moving atoms and molecules – Hot material energy has more energy available

which can be used for •  Chemical reactions •  Nuclear reactions (at very high temperature) •  Escape of gasses from planetary atmospheres •  Creation of light

–  Collision bumps electron up to higher energy orbit –  It emits extra energy as light when it drops back down to

lower energy orbit –  (Reverse can happen in absorption of light)

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Temperature Scales

•  Want temperature scale where energy is proportional to T –  Celsius scale is “arbitrary” (Fahrenheit even more so)

•  0o C = freezing point of water •  100o C = boiling point of water

–  By experiment, available energy = 0 at “Absolute Zero” = –273oC (-459.7oF)

–  Define “Kelvin” scale with same step size as Celsius, but 0K = -273oC = Absolute Zero

•  Use Kelvin Scale for most of work in this course –  Available energy is proportional to T, making equations simple

(really! OK, simpler) –  273K = freezing point of water –  373K = boiling point of water –  300K approximately room temperature

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Planck “Black Body Radiation”

•  Hot objects glow (emit light) –  Heat (and collisions) in material causes electrons to jump to high energy orbits –  As electrons drop back down, some of energy is emitted as light.

•  Reason for name “Black Body Radiation” –  In a “solid” body the close packing of the atoms means than the electron orbits are

complicated, and virtually all energy orbits are allowed. So all wavelengths of light can be emitted or absorbed. (In a gas with isolated atoms, only certain orbits are permitted so only certain wavelengths can be absorbed or emitted.)

–  A black material is one which readily absorbs all wavelengths of light. These turn out to be the same materials which also readily emit all wavelengths when hot.

•  The hotter the material the more energy it emits as light –  As you heat up a filament or branding iron, it glows brighter and brighter

•  The hotter the material the more readily it emits high energy (blue) photons –  As you heat up a filament or branding iron, it first glows dull red, then bright red,

then orange, then if you continue, yellow, and eventually blue

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Planck and other Formulae

•  Planck formula gives intensity of light at each wavelength –  It is complicated. We’ll use two simpler

formulae which can be derived from it.

•  Wien’s law tells us what wavelength has maximum intensity

•  Stefan-Boltzmann law tells us total

radiated energy per unit area

T Km 000,3

T Knm 000,000,3

Maxµ

λ ==

) Ks J/(m 105.67 where 42-84 ×== σσ TE


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Example of Wien’s law

•  What is wavelength at which you glow? –  Room T = 300 K so

–  This wavelength is about 20 times longer than what your eye can see. Camera in class operated at 7-14 µm.

•  What is temperature of the sun – which has maximum intensity at roughly 0.5 µm?

m10 K300

Km 000,3T

Km 000,3Max µ

µµλ ===

K000,6m 5.0

Km 000,3 Km 000,3

Max

===µµ

λµT


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Example of the Stefan-Boltzmann law

•  Suppose a brown-out causes the temperature of a lamp filament to drop to 0.9 of its original value. By what factor does the light output of the lamp drop?

•  Using the Stefan-Boltzmann law (with the numerical value of σ) we could have calculated how big (in m2) a light filament would have to be to emit 100 W of light, at any given temperature.

•  We could also use it to find the size of a star, if we know how much light energy that star emitted

66.0)9.0( 44

4

4

4

4

==⎟⎟⎠

⎞⎜⎜⎝

⎛===

I

F

I

F

I

F

I

F

TT

TT

TT

EE

σσ


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Kirchoff’s laws

•  Hot solids emit continuous spectra

•  Hot gasses try to do this, but can only emit discrete wavelengths

•  Cold gasses try to absorb these same discrete wavelengths

•  In stars we see absorption lines – what does that tell us? –  Stars have “atmospheres” of gasses –  Stars must be colder on the outside, hotter on the inside

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Hydrogen Lines

•  Energy absorbed/emitted depends on upper and lower levels •  Higher energy levels are close together •  Above a certain energy, electron can escape (ionization)

•  Series of lines named for bottom level –  To get absorption, lower level must be occupied

•  Depends upon temperature of atoms –  To get emission, upper level must be occupied

•  Can get down-ward cascade through many levels

From our text: Horizons, by Seeds n=1

n=2

n=3

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Which levels will be occupied?

•  The higher the temperature, the higher the typical level –  Collisions can knock electrons to higher levels,

if moving atoms have enough kinetic energy –  At T ~ 300 K (room T) almost all H in ground state (n=1) –  At T ~ 10,000 K many H are in first excited state (n=2) –  At T ~ 15,000 K many H are ionized

•  Because you have highest n=2 population at ~10,000K you also have highest Balmer line strength there.

•  This gives us another way to estimate temperatures of stars


n=1

n=2

n=3

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Sense larger T range using many atoms

•  Different atoms hold on to electrons with different force –  Use weakly held electrons to sense low temperatures (Fe, Ca, TiO)

•  TiO molecule is destroyed above 4000K •  Ca has lost 1 electron by ~5000K, but still has others to give lines

–  Use moderately held electrons to sense middle temperatures (H) •  Below 6000 K most H electrons in lowest state – can’t cause Balmer lines •  Above 15,000K most H electrons completely lost (ionized)

–  Use tightly held electrons to sense high temperatures (He, ionized He) •  Below 10,000K most He electrons in ground state – just like H, no visible absorption lines •  Above 15,000K most H has lost one electron, but still has a second one to cause absorptions


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Classification of stars

•  O B A F G K M scheme –  Originally in order of H strength – A,B,etc

Above order is for decreasing temperature –  Standard mnemonic: Oh, Be A Fine Girl

(Guy), Kiss Me –  Use numbers for finer divisions: A0,

A1, ... A9, F0, F1, ... F9, G0, G1, ...


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Composition of Stars

•  Somewhat complicated – we must correct for temperature effects •  Regular pattern:

–  More of the simplest atoms: H, then He, ... –  Subtle patterns later – related to nuclear fusion in stars


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Doppler effect

•  Effect similar in light and sound –  Waves compressed with source moving toward you

•  Sound pitch is higher, light wavelength is smaller (bluer) –  Waves stretched with source moving away from you

•  Sound pitch is lower, light wavelength is longer (redder)

•  v = velocity of source •  c = velocity of light (or sound) •  λ = apparent wavelength of light •  λo = original wavelength of light

0

0

0 λλλ

λλ −=

Δ=

cv

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Doppler effect examples

•  Car with horn blowing, moving away from you at 70 MPH. –  Speed of sound is ~700 MPH = 1000 ft/sec –  Original horn pitch is 200 cycles/sec ⇒ λo ~ 5 ft

•  Star moving toward you at 200 km/sec = 2.0×105 m/s –  Speed of light c = 3.00 × 108 m/s –  Original Hα λo= 0.65647 µm

1.0 MPH700 MPH701

00

0 ===−=−

cv

λλ

λλλ

ft 5.51.1 1.01 00

=×=+= λλλλ

00067.0m/s 103.00m/s 1000.21 8

5

00

0 −=××−

==−=−

cv

λλ

λλλ

m65603.099933.0 99933.000067.01 00

µλλλλ

=×==−=

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