Astro 1050 Fri. Sep. 30, 2005

Today: Extra Credit Articles

Finish Ch. 5

Start Chapter 6: Starlight and Atoms

The Highest Tech Mirrors Ever!

Chandra is the first X-ray telescope to have image as sharp as optical telescopes.

Spitzer Space Telescope

Heir to 1980s IRAS mission.

Mid to far IR.

Only 60 cm, Earth-trailing orbit, 5 year lifetime.

Imaging and mid-R spectroscopy.

DUST is important!

Spitzer Space Telescope

Discovered by a Wyoming grad student and professor. The “Cowboy Cluster” – an overlooked Globular Cluster.

Kepler’s Supernova with all three of NASA’s Great Observatories

Just 400 years ago: (Oct. 9, 1604)

Then a bright, naked eye object (no telescopes)

It’s still blowing up – now 14 light years wide and expanding at 4 million mph.

There’s material there at MANY temperatures, so many wavelengths are needed to understand it.

A Multiwavelength Look at Cygnus A

A merger-product, and powerful radio galaxy.

Radio Telescopes

Chapter 6: Starlight and Atoms
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

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

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 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 Þ Nucleus, Planets Þ 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.

Atoms – Constituent Parts I

Atoms contain 3 kinds of particles:

Electrons – in orbits Negatively charged Very low mass (1/1836 m_p)

Protons -- in nucleus Positively charged More “massive”

Neutrons – in nucleus Electrically neutral m_n » m_p

Atoms – Constituent Parts II

# of protons (Z) determines charge of nucleus Þ electrical properties Þ element

Chemical reactions involve sharing/exchanging electrons (See periodic table A-16)

Hydrogen: Z=1

Helium:      Z=2

Lithium:     Z=3

Carbon:      Z=6

Atoms – Constituent Parts III

# of protons and # of neutrons   determines mass and nuclear properties

Same element (same Z) but different # of neutrons Þ 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 = ???

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.

As 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.

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)

Temperature Scales

Want temperature scale where energy is proportional to T

Celsius scale is “arbitrary” (Fahrenheit even more so)

0^o C = freezing point of water

100^o C = boiling point of water

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

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

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.

Planck “Black Body Radiation”

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

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

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 mm?

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 s) 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

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

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

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

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

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, ...

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

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)

l = apparent wavelength of light

l_o = original wavelength of light

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 Þ l_o ~ 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 Ha l_o= 0.65647 mm


	Today: Extra Credit Articles
	Finish Ch. 5
	Start Chapter 6: Starlight and Atoms


	Chandra is the first X-ray telescope to have image as sharp as optical telescopes.


	Heir to 1980s IRAS mission.
	Mid to far IR.
	Only 60 cm, Earth-trailing orbit, 5 year lifetime.
	Imaging and mid-R spectroscopy.
	DUST is important!


	Discovered by a Wyoming grad student and professor. The “Cowboy Cluster” – an overlooked Globular Cluster.


	Just 400 years ago: (Oct. 9, 1604)
	Then a bright, naked eye object (no telescopes)
	It’s still blowing up – now 14 light years wide and expanding at 4 million mph.
	There’s material there at MANY temperatures, so many wavelengths are needed to understand it.


	“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


	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


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 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 Þ Nucleus, Planets Þ 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.



	Atoms contain 3 kinds of particles:
		Electrons – in orbits Negatively charged Very low mass (1/1836 m_p)
		Protons -- in nucleus Positively charged More “massive”
		Neutrons – in nucleus Electrically neutral m_n » m_p




	# of protons (Z) determines charge of nucleus Þ electrical properties Þ element
		Chemical reactions involve sharing/exchanging electrons (See periodic table A-16)
		Hydrogen: Z=1
		Helium: Z=2
		Lithium: Z=3
		Carbon: Z=6



	# of protons and # of neutrons determines mass and nuclear properties
		Same element (same Z) but different # of neutrons Þ 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 = ???



	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.
	As 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.



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)



Want temperature scale where energy is proportional to T
	Celsius scale is “arbitrary” (Fahrenheit even more so)
		0^o C = freezing point of water
		100^o C = boiling point of water
	By experiment, energy = 0 at “Absolute Zero” = –273^oC (-459.7^oF)
	Define “Kelvin” scale with same step size as Celsius, but 0K = -273^oC = 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



	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



	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



	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 mm?



	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 s) 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



	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



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



	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



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



	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, ...



	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



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)
		l = apparent wavelength of light
		l_o = original wavelength of light



	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 Þ l_o ~ 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 Ha l_o= 0.65647 mm