Matter and atomic structure Blackbody radiation Spectral lines States of matter.

Matter and atomic structureMatter and atomic structure

•Blackbody radiation•Spectral lines•States of matter

ReviewReview

•Resonances cause certain orbits to be either stable or unstable

This gives rise to ring gaps, asteroid belt, etc. Can eject bodies from the solar system

•Tidal forces Control rotation of some moons and planets Can be a strong source of internal heating (e.g. Io) Make it difficult to form large bodies (e.g. moons) within the

Roche limit

•Radiation pressure and the solar wind can drive small particles out of the solar system

Today’s lectureToday’s lecture

•What is the solar system made of? What are the elements?

The wave nature of lightThe wave nature of light

http://micro.magnet.fsu.edu/primer/java/polarizedlight/emwave/

Brief review:

The wavelength of light (λ) is related to frequency () by

A photon’s energy is given by:

c

hE

http://micro.magnet.fsu.edu/primer/java/polarizedlight/emwave/

Atmospheric transparencyAtmospheric transparency

The Earth’s atmosphere blocks most wavelengths of incident radiation very effectively. It is only transparent to visual light (obviously) and radio wavelengths.

Observations at other wavelengths have to be made from space.

Properties of blackbody radiationProperties of blackbody radiation

1. The wavelength at which radiation emission from a blackbody peaks decreases with increasing temperature, as given by Wien’s law:

K cm 290.0max T

42

4

4 e

e

TR

TAL

2. The total energy emitted (luminosity) by a blackbody

with area A increases with temperature (Stefan-Boltzmann equation)This defines the effective temperature of a star with radius R and luminosity L

ExamplesExamples

Although nothing in the Universe is a perfect blackbody (they always absorb certain wavelengths of light more efficiently than others), we can get some insight into the radiative properties of most objects

The human body has a temperature of 37 C, or 310 K. Calculate the total power radiated, and the rate of net energy loss. At what wavelength is this energy radiated?

K cm 290.0max T424 eTRL

ExamplesExamples

The sun has a luminosity L=3.826×1026 W and a radius R=6.96 ×108 m. What is the effective temperature? At what wavelength is most of the energy radiated?

K cm 290.0max T424 eTRL

SpectroscopySpectroscopy•Although astronomy has been practiced for thousands of years, it consisted mostly of observing and cataloguing the motions of stars.

•The use of spectroscopy to determine the properties of stars (c.a. 1814) allowed astronomers to investigate the the stars scientifically.

The solar spectrum

SpectroscopySpectroscopy

In 1814, Joseph Fraunhofer catalogued 475 sharp, dark lines in the solar spectrum.

• Discovered but misinterpreted in 1804 by William Wollaston• Spectrum was obtained by passing sunlight through a prism

Spectral linesSpectral lines

The wavelength of one particular line in the solar spectrum (at 589 nm) was found to be identical to the wavelength emitted by sodium (for example when salt is sprinkled on a flame).

Bunsen & Kirchoff designed a spectroscope and studied the wavelengths of light emitted and absorbed by various elements

Na D

Atomic spectroscopyAtomic spectroscopy

Bunsen & Kirchoff found that each atom emits light in a unique spectral fingerprint:

Neat java tool

The spectrum of a Helium lamp obtained by grating spectroscopy.

http://javalab.uoregon.edu/dcaley/elements/Elements.html

Kirchoff’s lawsKirchoff’s laws

1. A hot, dense gas or hot solid object produces a continuous spectrum with no dark spectral lines (a blackbody)

2. A hot, diffuse gas produces bright spectral emission lines

3. A cool, diffuse gas in front of a source of a continuous spectrum produces dark absorption lines in the continuous spectrum

Atomic absorption and emissionAtomic absorption and emission•The electrons of an atom occupy restricted regions around the

nucleus – called shells, or orbitals, or energy levels. •Generally the electrons occupy the lowest possible

orbital/energy level but they will sometimes change to a higher level if they gain enough energy from an incoming photon.

•The photon must have the right amount of energy to match the energy difference between the electron’s first energy state and the one it moves to.

c

hE2

c

hE2

• When this transition occurs, energy at the specific transition frequency is lost from the radiation field –absorption has occurred.

• An excited electron will readily drop down to a lower energy level, emitting radiation of a frequency/wavelength corresponding to the energy difference – emission.

Spectral analysisSpectral analysis

Thus the identification of absorption lines in stellar spectrum can tell us about the chemical composition of stars

The presence of unidentifiable absorption lines in the Sun’s spectrum led to the prediction of a new element, Helium (from Helios = Sun). Later this was isolated on Earth and the prediction was confirmed.

(However a similar, later prediction for a new element called coronium was found to be false. These lines are due to iron but under conditions not found on Earth)

Example: the solar spectrumExample: the solar spectrum

What elements are present in the Sun?

Solar spectrum



Balmer lines



NaD



Ca H+K


So: the Sun is mostly calcium, iron and sodium?? No! Not quite that simple…

Solar spectrum

MoleculesMolecules

•Like atoms and ions, molecules also emit or absorb light at specific wavelengths, corresponding to different rotational and vibrational states.

•The energy jumps in molecules are usually smaller than those in atoms and therefore produce lower-energy photons. Thus, most molecular bands lie in the infrared rather than in the visible or ultraviolet.

This spectrum of molecular hydrogen (H2) shows that molecular spectra consist of lines bunched into broad molecular bands.

Doppler shiftsDoppler shifts

Doppler shifts of the spectral lines yield the radial (i.e. toward the observer) velocity of the star

1 if

1)1(

1)1(

/1

/1

2

2

zz

z

z

c

v

z

cv

cv

r

restrest

restobs

r

rrestobs

1. Typical stars in the solar neighbourhood have velocities ~25 km/s. What is the size of their doppler shift?

Doppler shifts: examplesDoppler shifts: examples

Doppler shifts: examplesDoppler shifts: examples

2. Extragalactic objects (mostly galaxies and quasars) are strongly redshifted due to the expansion of the Universe. The most distant object currently known is quasar SDSS1148+5251, with z=6.42. Since z is not small, we have to use the full expression:

Elemental abundancesElemental abundances

•The chemical compositions we find for stars and gas clouds are somewhat surprising: ≥98% of the mass is made up of hydrogen and helium alone!

•The elements which are most abundant around us, such as carbon, nitrogen, iron …, represent only 2% (or less) of the matter in the Universe.

• This abundance picture is true for our Sun but not for most members of the SS. How can that be? Why is our Earth so different in composition from the Sun and other components of the galaxy in which we exist?

States of MatterStates of Matter

•Matter can be in different states, depending on how tightly bound the atoms are.

•Changes in phase require the breaking of a binding force

•For our purposes, we are mostly concerned with gases, solids and (to a lesser extent) liquids.


•Matter can coexist in different phases. At the triple point, gas, solid and liquid coexist.

Phase diagram for water


• The phase diagram for different elements tells us what phase they will be found in under given conditions.

• Knowing the triple point and critical point alone allow a rough estimate of the phase diagram.

Phase diagram for water Phase diagram for hydrogen

GasesGases

Ideal Gas Law: relates pressure, density and temperature

Hm

kTnkTP

Where n is the number density and is the mass density of the gas. is the mean molecular weight.

• Such an equation, relating pressure, density and temperature, is known as an equation of state.

• The equation of state for solids and liquids is generally much more complex and/or poorly known.

SolidsSolids

•Minerals are substances that occur naturally and include no organic (animal or vegetable) compounds.

The most commonly occurring minerals are made of the most commonly occurring elements”

In the inner SS these are dominantly O, Si, Mg, and Fe with lesser amounts of things like Na, Al, Ca, and Ni.

The minerals we find are vastly dominated by SiO4 – these are called silicates.

•Rocks are solids made of more than one mineral and the mix of minerals in rocks varies from one part of the SS to another and well as within a given body.

•Ices are solids whose composition consists of the abundant elements C,N,O in combination with H.

These compounds (water, carbon dioxide, methane, ammonia etc.) freeze at different temperatures; strictly speaking these are also minerals but are referred to as ices because of their low solidification temperatures.

Most common in the outer SS beyond ~3AU from the Sun.

SilicatesSilicates

Feldspars• SiO2 + K, Al, Na, Ca…• Least dense silicate• Low melting point

Pyroxene• chains of SiO4 +

Fe, Mg, Al, Ca…

Olivine• simplest silicate• SiO4 + Fe and/or

Mg• Most dense

silicate• High melting point

•The main silicate families are olivines, pyroxenes and feldspars. They are distinguished from each other by which elements are present and how complex are their crystalline structures.

RocksRocks

•Igneous Formed directly from cooling

of molten magma

•Sedimentary Deposition or cementing of

small particles

•Metamorphic rocks Originally formed as igneous

or sedimentary, but changed to a new form by high pressure, high temperature or addition of new chemicals

IcesIces

•solids that contain C,N,O – which are gaseous at T≥200K•CNO overall more abundant than Fe,Mg,Ca,Al,Na…

but Fe,Mg,…condense into grains at much higher T• ices are more abundant in outer SS objects – i.e. satellites,

comets, some asteroids, Kuiper Belt…•commonest ices: CH4 (methane), NH3 (ammonia), H2O (water)•vapourous “at the least excuse”

•Core of Halley’s comet shown outgassing as Sun heats the ice

Next LectureNext Lecture

The Sun and other stars•Colours and luminosities: the Hertzsprung-Russel diagram•Hydrostatic equilibrium•The source of stellar luminosity•Energy transport•The lifetime of stars

Matter and atomic structure Blackbody radiation Spectral lines States of matter.

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