Study Guide for Test #2

Dr. J. R. Webb

Stellar Astronomy

Chapter 5. The Nature of Light

The Speed of Light

· Light move at a speed of 186,000 miles per second.

· Galileo tried to measure light, but failed due to his inability to measure time accurately enough.

· Olaus Roemer measured the speed of light in 1673 by observing the moons of Jupiter.

The Nature of Light

· Isaac Newton postulated that light consists of particles by watching the dispersion of white light as it passes through a prism.

· Christianus Huyghens thought light was made of “waves”

· Thomas Young proved light had a wave nature in 1801 by performing the dual-slit experiment.

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Waves

· Transverse waves – the vibration is perpendicular (90^o angle) to the direction of motion.

· Longitudinal waves – The vibration is parallel (0^o angle) to the direction of motion.

· Frequency – how many crests pass per unit time

· Wavelength – physical distance between two crests

· Amplitude – how high the vibration gets from the average level.

· Speed – how fast does the wave disturbance travel.

For any wave: speed = wavelength x frequency or using symbols: v = ln

For light: c = ln, where c = 186,000 miles/second

James Clerk Maxwell realized that the waves predicted by Electro-magnetic theory are light waves. His equations predict:

• Electro-Magnetic waves move at the speed of light
• Propagate through a vacuum
• Have no restrictions as to how large or small the wavelengths can be. (see Figure 5-7 in the book.
1. radio waves – low frequency end of the spectrum, long wavelength.
2. visible light – region of the E-M spectrum our eyes are sensitive to.
3. gamma-ray – high frequency end of the spectrum, short wavelengths.

Units of measure used for light: 1 nanometer = 1nm = 10^-9 meters

1 angstrom = 1A = 10^-10 meters

visible light has wavelengths from: red: 7000 A to blue: 4000A

How does light interact with Matter?

Temperature: All substances are made up of atoms. The motions of these atoms is a measure of the heat content or temperature.

Hot gases –atoms are moving fast.

Cool gas – atoms are moving more slowly.

Temperature scales: Fahrenheit: 32^o F water freezes, 212^o F water boils

Celsius: 0^oC water freezes, 100^oC water boils

Kelvin: 0 K absolute zero, 273 K water freezes, 373 K water boils

Blackbody - An idealized object that can emit light but doesn't reflect any. In other words, absorbs all light that falls on it. Stars are good blackbodies.

Stefan-Boltzmann law – An object emits (energy) light at a rate proportional to the fourth power of its temperature (in Kelvins). This equation tells you how much energy your object emits in the form of light due to its temperature. It doesn't tell you anything about its frequency or wavelength though.

E = s T⁴ , where E = energy in Watts/meter²,

s = stefan-Boltzmann constant

= 5.67x10^-8 Watts/meter²-K⁴

T = temperature in Kelvins

Weins Law - The dominant wavelength (l_max) of radiation emitted by a blackbody is inversely proportional to its temperature.

l_max(meters) = 2.9x10^-3/ T(k) , where l_max is the maximum

wavelength measured in meters and

T is the temperature measured in

degrees Kelvin.

The Stefan-Boltzmann law and Wein's Law describe the basic properties of light light emitted by a blackbody. They were determined in laboratories, they were not derived from theory.

The wave theory of light was unable to account for Stefan-Boltzmann and Wein's Laws, or the shape of the blackbody curve (brightness as a function of wavelength).

Max Planck assumed: Electro-magnetic energy is emitted as wave packets or quanta called photons. The energy of a "quanta" or particle of light is given by:

E = hn = hc/l, where h = plancks constant = 6.625x10^-34 joules-s

c= speed of light

E = energy in a photon with frequency n or

wavelength l

Einstein verified this equation by explaining the photoelectric effect (for which he received the nobel prize in physics!

Photoelectric effect - Electrons in a metal sheet absorb energy from light depending on the frequency of the light, not on the intensity (brightness).

Using Planck's law you can derive Stefan-Boltzmann and Wein's Laws, and the shape of the blackbody curve!

Spectral Analysis

Fraunhoffer used a prizm to break the Sun's spectrum into its colors and noticed hundreds of dark lines, i.e. frequencies at which light is missing!

Kirchhoff's of spectral analysis:

1. A hot, glowing object emits a continuous spectrum.
2. when a continuous spectrum of light passes through a cool gas, dark lines called absorption lines appear in the continuous spectrum.
3. When a gas is heated to a high temperature, it radiates a bright line or emission lines spectrum.

Atomic Structure - Rutherford conculded from experiments with radioactivity that:

• Most of the mass in an atom is located in the nucleus
• Most of the atom is empty space, i.e. the nucleus is small compared to the size of the atom.

The nucleus contains the proton (electrically positive) and the neutron (electrically neutral). The neutrons and protons are responsible for 99.89% of the mass of the atom and the number of protons is indicative of the element (type of atom, examples are hydrogen (1 proton) or helium (2 protons) or oxygen).

Electrons exist in the atoms in orbits (more accurately energy levels) surrounding the nucleus. The energy of these levels depend on the nucleus and the electron can only occupy these quantized levels, i.e. cannot go half way! They require energy to move up a level and can absorb a photon with precisely that energy (remember Planck's law!).

• Each element has specific electron energy levels, therefore can absorb specific photons.
• Each electron tries to return to the ground state, and must do so by emitting a photn with the precise amount of energy.

Thus: absorption lines -- an electron absorbs a photon and jumps up a level.

emission lines -- an electron drops down an energy level and emits a photon to

carry off the energy!

Electrons can also move up energy levels by colliding with other atoms and absopbing Kinetic energy.

Ionization occurs when an electron obtains so much energy is leaves the atom, i.e. escapes!

Spectral series indicates transition from upper energy levels to a base level, Balmer series of hydrogen is all transitions where the electron lands on level is n=2.

Doppler Shift - The change in wavelength of a wave due to the motion of the observer or motion of the light source.

Dl/l = v/c

where: Dl is the change in wavelength of the original wave of wavelength l, v is the speed of the source or observer, and c is the speed of light.

Chapter 6.

Refraction - the bending of light due to the fact it slows down while going through a dense medium.

Refracting telescopes - made using lenses that cause all light incident to come to a focus at a particular spot (the focal point). The distance between the lens and the focal point is called the focal length. The refracting telescope contains an objective lens and an eyepiece.

The focal lenght of the objective lens

Magnification = ------------------------------------------------

The focal length of the eyepiece

Large Refractors are no longer built because of:

1. Light loss in the objective lens
2. large lenses are expensive and hard to make
3. glass is opaque to certain frequencies (not trqansparent)
4. Chromatic aberration - you can only make 1 frequency focus at a time because of dispersion, different frequencies slow by different amount in glass,
5. LArge mechanical support mechanisms are need due to the weight of glass.

Relfecting Telescope - telescopes made using the property of reflection of light off a surface. Angle of incidence = angle of reflection. No chromatic aberration!

Has a primary mirror for collecting light, a secondary mirror for reflectig the focal point, and an eyepiece.

Types of Reflecting Telescopes - Newtonian, Cassegranian, prime focus. (see diagrams in the book!)

Light Gathering Power - the amount of photons your telescope collects depends on the AREA of the primary mirror. (Area = 4 p r²)

The resolving power of a telescope depends on the focal ratio (f), the waelength of light being observed l and the diameter d of the objective lens or primary mirror.

RP = 1.22 l f / d

You want RP to be small since RP represents the smallest angle at which you can see two sources as individually distinct.

Slide Show: we saw observatories on mountain tops, radio arrays and interferometers, and satellite telescopes. Interferometers are individual mirrors whose signals are added together to produce the resolving power of a single telescope the size of the distance between the individual mirrors.

Chapter 16 – The Sun

The Sun is an average Star: average size, mass, luminosity (brightness), and chemical composition.

The structure of the Sun is a “Rosetta Stone” for studying stars. The Sun is so close, we can see it very clearly.

• The Solar Interior. – Geologists can show the Earth has existed at its present temperature for billions of years, thus the Sun must have been shining at its present rate for that long. Fossil Fuels are too inefficinent, cannot produce enough energy.

Einstein’s E=mc² allowed us to understand nuclear reactions, and in 1920’s Sir Arthur Eddington calculated the temperatures and pressures in the center of the Sun if it were made of pure hydrogen: T ~ 15,000,000 K!

At 15 million Kelvins, 4 hydrogen nuclei combine to form 1 helium nucleus:

4 Hydrogen = 4 protons = 6.693x10^-24 grams

1 Helium = 2 protons + 2 neutrons = 6.645x10^-24 grams

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subtracting the masses gives : mass lost = 0.048x10^-24 grams

Thus 0.048x10²⁴ grams of mass is converted into energy by E = mc², or E = (0.048x10^-24)(2.99x10¹⁰)²

This gives E = 3.2x10^-5 ergs and the Sun emits 3.0x10³³ ergs/sec, so about 10³⁸ reactions occur every second.

In other words, 600 million tons of hydrogem burns to Helium every second!!!!!!!

(1 erg= the energy possessed by a 2 gram mass moving at 1 cm/sec.)

During the reaction, two of the protons (hydrogen nuclei) are converted to neutrons (helium nucleus is 2 protons and two

neutrons) by emitting positrons (+ electrons which carry off the positive electric charge) and other particles called

neutrinos. The neutrinos emerge from the Sun, go through the Earth and other planets never stopping.

• Equations of Stellar Structure: -
1. Hydrostatic equilibrium – gas pressure balances gravity
2. Thermal Equilibrium - Energy that escapes the Sun must be equal to the energy generated in the interior.
3. Energy transport – Conduction, convection or radiative diffusion
4. Conservation of Mass – Mass is conserved at every point except where nuclear reactions are occurring.

Voight-Russell Theorem – The structure and evolution of a star is totally dependant in its mass and chemical composition!

• Photosphere - visual surface of the Sun, R = 696,000 lm, T = 5,800 Kelvins.

Limb darkening is the effect we see since we see different photospheric layers at different angles. The bottom of the photosphere is hotter, 8000K, while the top is cooler 4400K.

• Granuals – or rice grain structure are the tops of the convective cells which brings energy up from below. Size ~ 1,000 Km, about 4,000,000 cells at any one time, lifetime ~ 8-15 minutes.

• Chromosphere – “sphere of color” thin tenuous gas layer that emits in H-alpha light and Ca H and K lines. (emission lines). Chromospheric features – plagues, filaments. Spicules – columns of gas that shoot through the chromosphere into the corona!

• Corona – Outer layers of the Sun which consists of tenuous, very hot (millions of kelvins) gas extends up several million Km from the chromosphere!

Solar activity is caused by magnetic disturbances!

• Sunspots – irregularly shaped dark regions in the Solar Photosphere (actually cooler than surrounding gas).
• Dark Central core – Umbra – T ~ 4300 Kelvins
• Lighter border of Spot – Penumbra – T ~ 5700 Kelvins

Sunspots occur in a cycle, they start at high latitudes, each spot lasts only a few months, then new spots form at lower latitudes. After 11 years, the cycle starts over again. (see butterfly diagram in book!).

Sunspots occur because magnetic field prevents hot gas from convecting to the surface, thus cooling off the surface in

That region. The Sun rotates differentially (on cylinders!), and magnetic field gets wrapped up, puncturing the Solar

surface and preventing convection. Thus, sunspots form. This is Babcock’s Magneto-hydrodynamic model!