# Exam One Info

### Contents of the Exam

The First Exam will cover material presented in the lectures, Chapters 1, 5, 6.3-6.4, and 14.

### Format of the Exam

The Exam will be true/false, multiple choice and short answer format. The previous homeworks and review questions at the end of the chapters will help you review the material. Below are a few sample questions to give you an idea of what to expect. These questions do, however, over-emphasize quantitative topics in order to give you additional practice on these.

### Physical Constants you do not need to remember

Speed of light, c = 3.0 x 105 km/s = 3.0 x 108 m/s.
Planck's constant, h = 6.62 x 10-34 J s (Joules x seconds).
Wein's constant, 2.9 x 106 nm K (nanometers x Kelvins).
Stefan-Boltzmann constant, sigma = 5.67 x 10-8 J/m2.K4.s
1 parsec = 3.08 x 1016m.

### Formulae you will be given

• Wave equation : c = fw     (c=speed of wave, f=frequency, w=wavelength)
• Photon energy : E = hf = hc/w     (h=Planck's constant)
• Temperature conversion : T(K) = T(C) + 273     (K=Kelvin, C=centigrade)
• Wein's law : wpeak(nm) = 2.9 x 106 / T(K)     (w is wavelength of peak of thermal spectrum, measured in nanometers).
• Stefan-Boltzman law : L = A s T4     (L= total power emitted by a black body of surface area A at temperature T(K), where s is the Stefan-Boltmann constant).
• Doppler shift : (w - w0) / w0 = vr/c     (where w is the observed wavelength, w0 is the original, ie rest, wavelength, vr is the componant of velocity towards (-ve) or away (+ve) from the observer, c=speed of the wave).
• Energy - mass relation : E = m c2     (keep units consistent : E(J) m(Kg) c(m/s) )

### Things to Know and Understand

Here is a list of the major themes we have discussed in class, presented partly in question form. This should give you some idea of the range and scope of the topics.

A. Be familiar with the Powers of 10 notation for numbers and be able to rearrange simple formulae to evaluate one of the terms. Know the various prefixes for large and small numbers (e.g. Giga- for billion)

B. Understand the basic nested sequence of structures and their sizes in the universe : planets, stars, galaxies, universe. Know the common units of distance that astronomers use (AU, lightyear, parsec).

C. Understand the concept of look-back time, and how astronomers can witness history by looking far away. Recognize that it is possible to see the Big Bang. Know the age of the Universe, the age of the Earth and, relative to these, the brevity of human existence.

D. Recognize the four ways light interacts with matter: emission, absorption, transmission, and reflection (scattering). Know why everyday objects appear to have color.

E. Know the basic properties of light: its speed, its wave-like and particle-like nature, its electromagnetic nature. Be able to put in sequence the various types of electromagnetic radiation (gamma, X-, ultra-violet, optical, infra-red, microwave, radio). Which of these can be observed from the ground and which must be observed from space ? For optical, know the sequence of colors in the rainbow and approximately the corresponding wavelengths in nanometers.

F. Understand what 'frequency' is, and know the relationship between wave speed, wavelength, and frequency. Approximately what is the frequency of visible light?

G. Understand the nature of photons, and the relationship between photon energy and frequency and/or photon energy and wavelength. In human terms, do photons of visible light carry much energy?

H. Know about the structure of atoms : nucleus, electrons, limited orbits, energy levels, the periodic table. How are photons emitted and absorbed? Know the energy level diagram of Hydrogen, and how it gives rise to sequences of emission lines. Know that different elements and ions each have a unique emission or absorption spectrum.

I. Know the difference between Celsius and Kelvin temperature scales, and why scientists like to use the Kelvin scale. Recognize that at any temperature there is a spread of particle speeds and energy, and the temperature is proportional to the average energy of the particles.

J. What is thermal radiation, and why is it generated ? Know the basic shape of a thermal (i.e. black body) spectrum. What is Wein's Law, and how can you deduce the temperature of an object from the peak color of its thermal spectrum. Know the Stefan-Boltzmann Law. How does the energy liberated by a hot surface depend on the temperature of that surface?

K. Understand what 'emission lines' and 'absorption lines' are, and the circumstances in which each are seen (i.e. Kirchoff's Laws).

L. Understand the Doppler effect, and how to calculate the speed of an object from its change in color (or more specifically, the shift of a spectral emission or absorption line). How can this be applied to measure the rotation rate of stars?

M. Know the Sun's approximate 'vital statistics' : size, mass, average density, luminosity, temperature, composition, rotation. Know its overall structure: core, radiative zone, convective zone, photosphere, chromosphere, corona. Understand what hydrostatic equilibrium is, and how the balance of gravity and pressure ensure the center of the sun is both dense and hot.

N. What is the sun's energy source (and why can't it be chemical or gravitational). Understand the difference between Fission and Fusion, and that nuclear reactions are energy rich compared to chemical reactions. Know and be able to evaluate Einstein's relation E=mc2. Know, approximately, the chain of reactions converting hydrogen into helium, and that overall 0.7% of the mass is converted into energy.

O. Understand what the solar thermostat is: how expansion or contraction of the core can keep the nuclear fusion reactions at a steady pace.

P. How does energy get from the center of the sun to the surface. Understand the difference between the radiation and convection zones, and how energy passes through them.

Q. How do we know about the interior of the Sun? Why are mathematical models of the sun's structure reliable? What is Helioseismology, how do astronomers "listen" to the vibrations of the sun, and what do they tell us about the Sun's interior? What are "Solar Neutrinos", how are they detected, and why might one be interested in measuring them?

R. Importance of magnetic fields for the solar "weather/storms". The nature of Sunspots; why are they cooler? Prominences, flares and coronal mass ejections. The 11 year sunspot cycle. Theory of activity cycles: amplification of magnetic field by differential rotation.

S. Know the Sun's four atmospheric components : photosphere, chromosphere, corona, solar wind. Know approximately their properties eg temperatures and depths. Is the corona hotter or cooler than the photosphere? How do bursts in the solar wind affect the Earth?

### Sample Questions

These questions emphasize the numerical topics to give you additional practice.

1. Practice at simple powers of 10 notation:

1. Write 0.0005 in scientific notation.
2. What is (3 x 103) x (4 x 10-4).
3. What is 1/(3 x 103).
4. What is (3 x 103)4.
5. What is (3 x 103)-2.

2. If the Sun is the size of a Grapefruit, the solar system would span a region the size of:

1. a table-top
2. a room
3. a football field
4. the University
5. the USA.

3. Roughly how many galaxies are in our observable universe?

1. 1 billion
2. 100 billion
3. 10 trillion
4. an infinite number, because the Universe is infinite.

4. T/F Green light has a lower frequency than red light.

5. An AM radio station has a frequency of 600 kHz (kilohertz). What is the wavelength of these radio waves ?

1. 2 x 10-3 meters
2. 1.8 x 10 13 meters
3. 1.8 x 10 6 meters
4. 500 meters

6. What is the fundamental difference between between X-rays and radio waves ?

1. they always come from different sources
2. their speeds in outer space are different
3. their wavelengths are different
4. radio waves are always waves, while X-rays always behave like particles

7. T/F The best ultraviolet telescopes are built on high mountains.

8. When electrons in Hydrogen atoms fall from level 4 to level 2, the energy they release is 4.09 x 10-19 Joules. (a) What is the frequency of the photon that is emitted (in Hz) ? (b) What is the corresponding wavelength (in nm) ? (c) What color does this correspond to ?

9. T/F Orange stars are hotter than yellow ones.

10. As long as you do not have a fever, your temperature is about 35 degrees C. (a) what is your temperature in degrees Kelvin ? (b) Use Wien's law to calculate the peak wavelength of your thermal radiation (in nm). (c) What part of the electromagnetic spectrum is this in ? (d) If the surface area of your skin is about 1 square meter (true for most adults), use the Stefan-Boltzmann law to estimate roughly how much thermal energy we radiate --- the answer should be in Watts (ie Joules/sec).

11. Two identical light bulbs are run such that the filament of one is three times as hot as the other (measured in degrees K). How much brighter is the hotter light bulb ?

12. How many electrons will surround the nucleus of a neutral atom of iron, the 26th element in the periodic table ?

1. 52
2. 27
3. 25
4. 26
5. 14

13. When an electron moves from one atomic orbit to another orbit with lower energy, which of the following occurs?

1. The atom absorbs an arbitrary wavelength of light.
2. The atom emits light with energy equal to the difference in the two orbits.
3. The atom becomes ionized.
4. The atom absorbs light with energy equal to the difference in the two orbits.

14. T/F Lyman absorption lines begin with the electron in a hydrogen atom in the ground state (level number 1).

15. Atoms in a thin hot gas, according to Kirchoff's laws, emit light

1. only at one specific, single wavelength color
2. at all wavelengths, the shape of the continuous spectrum depending on the temperature of the gas
3. only at visible wavelengths
4. with all colors except at certain specific wavelengths
5. at specific wavelengths, the pattern depending on the element

16. If a certain emission line that has a rest (zero velocity) wavelength of 500 nm is observed to have a wavelength of 700 nm in a certain star, that star is moving at a velocity of

1. 1.2 x 105 km/sec away from us
2. 1.2 x 105 km/sec towards us
3. 8.5 x 104 km/sec away from us
4. 2.1 x 105 km/sec away from us

17. T/F According to Wien's law, a blue piece of paper is hotter than a red piece of paper.

18. State briefly why many gaseous nebulae appear red in color.

19. T/F The earth's (almost circular) orbital speed about the sun is about 36 km/s. Because of this high speed, the absorption lines from the sun appear to us to be slightly blueshifted.

20. Name three parts of the electromagnetic spectrum which cannot pass through the earth's atmosphere to reach the ground.

21. T/F Inside atoms, about half the space is taken up by the nucleus and the other half by the electrons.

22. T/F An ion is an atom with a net positive or negative charge.

23. The moon is half a degree across, as seen from the earth. How many arcseconds is this ?

24. Use Kirchoff's laws to explain why the spectra of stars have absorption lines.

25. In the Earth's atmosphere, nitrogen and oxygen are the two most abundant elements. Which two elements are the most abundant in the atmosphere of the sun ?

26. The density of gas in the photosphere of the Sun is

1. much less than the density of air (at sea level);
2. similar to air at sea level
3. similar to water

27. Of the solar zones listed here, the hottest is

1. the chromosphere
2. the corona
3. the photosphere

28. T/F The Aurora Borealis (Northern Lights) are strongest at times of maximum solar activity.

29. Which of the following is NOT true about solar activity?

1. The two members of a sunspot pair usually have opposite magnetic polarity.
2. Solar flares are common when there are many sunspots.
3. Sunspots gradually shift their locations from high latitudes towards the equator.
4. Sunspot storms rotate clockwise in the sun's northern hemisphere and counter clockwise in the sun's southern hemisphere

30. If 1 kg of hydrogen is completely converted into energy, how much energy (in Joules) is created ? If 1 kg of hydrogen is converted into helium, approximately how much energy is released ?

31. Nuclear reactions which power the Sun convert

1. a helium nucleus into hydrogen nuclei
2. four hydrogen nuclei into one helium nucleus
3. a hydrogen nucleus into a helium nucleus
4. deuterium into hydrogen

32. What is Hydrostatic Equilibrium and what property of the sun does this give rise to.

33. Energy is transported in the Sun by

1. convection in the deep interior and radiative diffusion in the outer layers
2. convection in the outer layers and radiative diffusion in the deep interior
3. radiative diffusion in the deep interior and neutrinos in the outer layers
4. convection in the deep interior and magnetic fields in the outer layers

Do the questions, write down your answers, then check yourself with these Answers Think about the ones you missed. If you feel you need help, don't forget my office hours (see syllabus for these) or set up an appointment (my office is 216 Astronomy Building).