# Exam One Info

### Contents of the Exam

The First Exam will cover material presented in the lectures, Chapters 1, 6.1, 7, 8, 9 (up to apparent and absolute magnitudes).

### Format of the Exam

The Exam will be true/false, multiple choice and short answer format. The 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.

Dont forget Dr Hawley's web resources, including a concise narrative of the material, as well as additional test questions. Although the material in those notes is essentially identical to ours, the order of the topics is slightly different (use your judgement to sort out what is relevant to our current exam). His main web page is here.

### 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 DO need to know

• 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).
• the Stefan-Boltzmann law applied to stars : L = 4 pi R2 s T4     (where the stars surface area is 4 pi R2 and R is the radius of the star).
• 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).
• Parallax relation : dpc = 1/parcsec     (d=distance in parsecs, p=parallax angle in arcsec).
• Energy - mass relation : E = m c2     (keep units consistent : E(J) m(Kg) c(m/s) )
• Luminosity brightness relation : L = 4 pi d2 b     (L is the luminosity, d is the distance to the object, b is its apparent brightness).

### Sample Questions

1a. Write 0.0005 in scientific notation.

1b. What is (3 x 103) x (4 x 10-4).

1c. What is 1/(3 x 103).

1d. What is (3 x 103)4.

1e. What is (3 x 103)-2.

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

3. 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

4. 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

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

6. 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 ?

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

8. 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).

9. Star A has a temperature of 7000 degrees Kelvin. Star B has a temperature of 3500 degrees. The radius of star B is 4 times that of Star A. Which statement is true?

1. The total energy emitted by A is twice that of B.
2. The total energy emitted by B is twice that of A.
3. The total energy emitted by A is 16 times that of B.
4. The total energies emitted by each star are equal.

10. 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 ?

11. 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

12. 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.

13. T/F Lyman absorption lines begin with the electron in the ground state (level number 1).

14. 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

15. 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

16. Why are the Balmer series of absorption lines from Hydrogen weak in very hot (O type) stars, strong in cooler (A type) stars, but weak again in even cooler (K type) stars ?

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. Use powers of 10 notation to estimate, roughly, the surface area of the earth in square meters, given that its radius is 6000 km.

21. Name three wavebands which cannot pass through the earth's atmosphere to reach the ground.

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

23. T/F An ion is an atom with a net positive or negative charge. How might an ion be produced from an atom ?

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

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

26. 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 ?

27. 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

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

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

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

30. 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

31. 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 ?

32. 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

33. T/F Pushing a star to 5 times its current distance, it will appear 5 times fainter.

34. T/F A 15th magnitude galaxy appears 1 million times fainter than the bright star Vega, which has magnitude 0.

35. T/F A K2 star is slightly hotter than a G2 star.

36. What spectral type of star has strong molecular absorption lines ?

37. T/F The absorption lines of red giants are narrower than the absorption lines of red main sequence stars.

38. A star has brightness 3 x 10-9 Watt/m2 and a parallax of 0.02 arcsec. What is its luminosity, in Watt and in Lsun ?

39. T/F A star with a parallax of 0.2 arcsec is 2 parsecs away.

### 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. It is compelmentary to the concept list you got at the beginning of the class, and should help you review the material.

A. 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).

B. Be familiar with the Powers of 10 notation for numbers and be able to rearrange simple formulae to evaluate one of the terms.

C. Know the basic properties of light : its speed, its wave-like and particle-like nature, its electromagnetic nature, how it is created. Know experiments that show wave behaviour and particle behaviour. Understand, roughly, what diffraction and interference are.

D. 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.

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

F. 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 ?

G. What is thermal radiation, and why is it generated ? What is a 'perfect' emitter/absorber and why is it called a 'black body'. Know the basic shape of a black body (ie thermal) spectrum.

H. What is Wein's Law, and how can you deduce the temperature of an object from the peak color of its thermal spectrum. Approximately, what is the correspondence between color and temperature.

I. Know the difference between Celsius and Kelvin temperature scales, and why scientists like to use the Kelvin scale.

J. Know the Stefan-Boltzmann Law. How does the luminosity of a star depend on its size and surface temperature ?

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

L. 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.

M. Know that a star's temperature determines the kind of absorption lines seen in its spectrum. Know the temperature sequence O,B,A,F,G,K,M and which absorption lines correspond (approximately) to which spectral type. Understand why the Balmer series has a maximum strength at A type stars.

N. Know about collisional line broadening -- atom collisions lead to a blurring of the atom's energy levels and hence a widening of the absorption lines. Know that large (small) stars have low (high) pressure atmospheres and hence narrow (broad) absorption lines.

O. Understand the Doppler effect, and how to calculate the speed of an object from its change in color. What is 'proper motion' and what is a typical value for nearby stars.

P. Know the Sun's approximate 'vital statistics' : size, mass, average density, luminosity, temperature, composition, rotation.

Q. Know the Sun's four atmospheric components : photosphere, chromosphere, corona, solar wind. Know approximately their properties eg temperatures and depths. Why is the chromosphere red ? How did Helium get its name ? Is the corona hotter or cooler than the photosphere ? How do we "see" the solar wind when it hits the earth?

R. Importance of magnetic fields for the solar "weather/storms". The nature of Sunspots; why are they cooler ? 11 & 22 year sunspot cycles. Theory of activity cycles --- amplification of magnetic field by differential rotation. Active regions : prominences, flares.

S. What is the sun's energy source (and why can't it be chemical or gravitational). The mass lost (0.7%) between four Hydrogens and one Helium gives the energy release. Know and be able to evaluate Einstein's relation E=mc2. Know, approximately, the chain of reactions converting hydrogen into helium.

T. 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 ?

U. How do we measure distances to stars; how is a "parsec" defined; know the relation between parallax angle (in arcsec) and distance to a star (in parsecs).

V. Know what "proper motion" is. Does it yield radial or transverse velocity ? Roughly, what might the proper motion of a nearby star be ?

W. What is the difference between a star's apparent brightness and its luminosity, and how are these two quantities related (know a formula which gives one in terms of the other). What is the inverse square law of brightness ?

X. Know the magnitude scale, its historical roots, and its more modern form. Are stars with small magnitudes brighter or fainter than those with large magnitudes ? Know that a difference of 5 magnitudes corresponds to a factor of 100 in brightness.

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, dont forget the TA office hours in room 267, Mon 5pm - 8pm, Tues 9am - 12pm, Wed 4pm - 7pm, Fri 2:30pm - 5:30pm. And my own office hours 2pm to 3pm (Wed, Thurs).