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Exam Technique READ THE QUESTION!! make sure you understand what you are being asked to do make sure you do everything you are asked to do make sure you do as much (or as little) as you are asked to do [implicitly, by the number of marks] Answer the question, the whole question, and nothing but the question Exam Technique Read the whole paper through before you start if you have a choice, choose carefully whether or not you have a choice, do the easiest bits first this makes sure you pick up all the “easy” marks PHY111 do all of section A (20 questions, 40%) do 3 from 5 in section B (3 questions, 30%) do 1 from 3 in section C (1 question, 30%) Last Year’s Exam, Section B Answer any 3 of 5 short questions 5 marks each exam is out of 50 i.e. 120/50=2.4 minutes per mark hence each question should take ~12 minutes to answer do not let yourself get bogged down, but do not write 2 sentences for 5 marks! Question B1 Briefly explain how you would go about determining the distance of a nearby star; [1] parallax, i.e. the apparent shift in the star’s position over the course of a year the surface temperature of a star; [1] either its colour or the strengths of spectral lines the surface chemical composition of a star. [2] the strengths of spectral lines [1] after correcting for temperature [1] Under what circumstances could you determine the star’s mass? [1] if it is a member of a suitable binary system Question B2 The Sun is a class G (yellow) main sequence star. Vega is a class A (white) main sequence star, while Aldebaran is a class K (orange) giant star. Both Vega and Aldebaran are considerably more luminous than the Sun. Explain carefully how you know that Vega is younger than the Sun. [2] From binary stars, white main-sequence stars are more massive than yellow main-sequence stars [½] and luminosity increases much faster than mass [½] so Vega must have a much shorter main-sequence lifetime than the Sun [½] and we know the Sun is halfway through its main sequence life, so Vega must be younger than the Sun [½] Question B2 Explain how you know that Aldebaran is physically larger (i.e. has a greater radius) than the Sun. [1] From blackbody spectra, red objects are cooler than yellow [½] and cooler objects emit less light per square metre, so in order to be brighter Aldebaran must have a much larger surface area. [½] Is Aldebaran (i) necessarily older than the Sun, (ii) necessarily younger than the Sun or (iii) either older or younger than the Sun – it is not possible to tell with only this information? Carefully explain your answer. [2] (iii) either older or younger [½] because red giant stars have similar brightnesses over a range of masses, [½] and therefore we do not know if Aldebaran is a massive star which will evolve quickly, or a low mass star which evolves slowly [1] Question B3 The table below shows the isotopes of indium, cadmium, silver, palladium and rhenium. Those marked ε decay by converting a proton to a neutron; those marked β decay by converting a neutron to a proton; those marked with a number are stable (the number is the percentage of the natural metal that is made of that isotope). Blank squares indicate nuclei so unstable they have never been seen. Study this table and answer the questions below. Question B3 Explain what is meant by the term s-process. Which stable isotopes of palladium (46Pd) are made by the s-process? [2] s-process: slow addition of neutrons (unstable isotopes decay before next neutron is added) [1] What is meant by the term r-process? Write down (i) a stable isotope of palladium which must be made by the r-process and (ii) a stable isotope of cadmium (48Cd) which cannot be made by the rprocess. [2] r-process: rapid addition of neutrons (forms unstable neutron-rich isotopes which then β-decay to stable isotopes) [1] Name one stable isotope shown on the table which cannot be made by either the s-process or the r-process, and name the process by which it is made. [1] Question B3 number of neutrons 53 54 55 56 57 58 59 60 49In 61 62 63 64 65 66 67 ε ε ε 4 β 96 β 29 β P ε 48Cd ε 1 ε P 47Ag 46Pd ε ε ε ε ε ε ε R 12 13 24 12 R ε ε ε ε 52 β 48 β β β 1 ε 11 22 27 β 27 β 12 β S S S 100 β β P 45Rh 1 ε ε R β R β direction of β decay Question B4 Explain the significance of any TWO of the following observations in the context of modern cosmology: the fact that the sky is dark at night; [2.5] the redshifts of galaxy spectra; [2.5] the properties of the cosmic microwave background; [2.5] the brightness of distant supernovae. [2.5] Question B4 the fact that the sky is dark at night; [2.5] In an infinite, eternal, static universe, every line of sight must at some point intersect a star, which would not give a dark sky. [1] Therefore, one or more of the assumptions is false: in the Big Bang model, the universe has finite age (light from distant stars may not have reached us) and is expanding (light from distant stars is redshifted to much cooler temperatures); [1] in the Steady State model, the universe is expanding. [0.5] Question B4 the redshifts of galaxy spectra; [2.5] Most galaxy spectra are redshifted, and the redshift is proportional to the distance of the galaxy. [1] This implies that the universe is expanding (it does not imply that we are near the centre). [0.5] In the Big Bang model, the universe cools and becomes less dense as it expands. [0.5] In the Steady State model, new matter is created, and the universe looks the same at all times. [0.5] You can get full marks for describing ONE property in DETAIL or two/three properties in outline. Question B4 the properties of the cosmic microwave background; [2.5] The CMB has the following properties: blackbody spectrum (2.74 K) this is important because it says that the radiation must have been created in a dense environment at one particular time in the past (good for Big Bang, bad for Steady State) near-uniformity over the whole sky this is surprising because different “sides” of the sky should never have exchanged photons, and therefore do not know each other’s temperature – it is one of the key pieces of evidence for inflation very small temperature fluctuations (1 in 100000) by studying these we can show that the universe is flat, and also measure many other cosmological parameters Question B4 the brightness of distant supernovae. [2.5] Type Ia supernovae all have very similar brightness, and are bright enough to be seen out to large redshifts, so can be used to check how the expansion of the universe changes with time. [1] Expected to find that the expansion is slowing down owing to gravity – in fact found that it was accelerating. [0.5] This is evidence for the existence of dark energy (Einstein’s cosmological constant, Λ), which we now think makes up ~70% of the energy density needed for the universe to be flat (as we see it to be). [1] Question B5 Most of the planets discovered around other stars have been detected using the spectroscopic (Doppler shift) method. Explain how this method works, and what kind of planetary systems it is most likely to detect. [2.5] Works by detecting the shift in the spectral lines of the parent star as it moves towards and away from us in its orbit around the star-planet centre of mass. [1] Requires orbit to be tilted relative to the plane of the sky (or no Doppler shift) [0.5] Most likely to detect massive planet close to star (in edge-on orbit) [1] Question B5 Briefly describe the properties of the detected extrasolar planets. With reference to your previous answer, discuss how these properties are likely to be biased by the detection method used. [2.5] Mostly large planets (at least Uranus/Neptune mass, up to several Jupiters; one or two only a few Earth masses) This is clearly biased by the detection method Mostly fairly close to star (within around 3 AU) – some very much closer (<0.1 AU) This is also biased by the detection method Many in eccentric (non-circular) orbits This is much less biased, though it does make detection easier Mostly only one planet per system (though up to 5) Not seriously biased Last Year’s Exam, Section C Answer any 1 of 3 long questions 15 marks each, ~36 minutes’ work Question C3 is on the seminars: Write short essays on any three of the following binary stars black holes the search for dark matter the search for life on Mars Note that you know this is coming, so more detail expected in answers! Question C1 The picture shows the Hertzsprung-Russell diagram for those nearby stars whose parallaxes were accurately measured by the HIPPARCOS satellite. Note that the Sun has absolute magnitude 4.8 and colour index B – V = 0.65. Question C1(a) The vast majority of the stars are on the main sequence. Explain what defines a main sequence star, in terms of its energy generation mechanism, and why we should expect most stars to be on the main sequence. [2] Fusion of hydrogen to helium in core of star [1] Hydrogen is the easiest element to fuse, the most abundant, and the most efficient energy generator – therefore expect this stage to last longest. [1] Question C1(b) Carefully explain what features of the diagram show that the stars included are not all of the same age, and, in particular, that they include stars which are much younger than the Sun. [3] Diagram contains both bright MS stars and faint giants [1] Mass-luminosity relation tells us bright MS stars have short lifetimes, hence these must be young (<< 4.6 Gyr old Sun!) [1] Faint giants evolve from relatively faint (hence long-lived) MS stars [1] these are HB stars, so are also older Question C1(c) What are the stars at the bottom left of the diagram, and what can you tell about them purely from their position on the diagram? [2] White dwarfs [0.5] They have high surface temperatures (because they are on the left-hand side of the diagram) [0.5] so, since they are nevertheless faint, they must be very small (as hot dense objects emit more light per square metre than cooler objects) [1] Question C1(d) Bearing in mind that HIPPARCOS had a relatively small telescope, do you expect this diagram to be a fair sample of the stars in the solar neighbourhood? If not, explain which stars will be undercounted, and why. [2] No [0.5] Intrinsically faint stars (lower MS, white dwarfs) will be undercounted [1] because they cannot be seen at large distances with a small telescope [0.5] Question C1(e) Describe the evolution of a star of ~2 solar masses, from its arrival on the main sequence to the end of fusion processes, including an account of the remnant left after fusion stops. Include a sketch of its trajectory on the HR diagram, and where possible relate your description to the features of the HIPPARCOS HR diagram shown above. [6] Note the key points in this question! Many students missed out on marks through NOT ANSWERING THE QUESTION! Question C1(e) 5. Eventually core He heats up enough to fuse. Star moves rapidly from tip of RGB to horizontal branch or red clump 1. On arrival on MS, star is fusing H to He in core. This stage lasts for ~90% of star’s life, which ex-6. When core He runs out, star starts fusing He plains why most stars are on MS 2. When core H exhausted, starin shell around core, becoming a giant again shrinks under gravity, heating up until H outside core starts to fuse. 4. H fusion in shell causes 7. During stage 6, star sheds most of its outer envelope owing to star to become brighter, instability. This exposes the extremely hot carbon core, whose ultraviolet ascending red giant radiation causes the expanding shell of and expelled gas to glow – a planetary 3. Star expands branch as seen in nebula. When the gas cools, shell has dissipated, is revealed moving right onthe cooling core HIPPARCOS diag. as a white dwarf at the subgiant bottom left of theofHR diagram. branch HR diagram Question C2(a) Describe, with appropriate diagrams, the Hubble tuning fork system for the classification of galaxies. [6] En where increasing n indicates increasing ellipticity. S0: disc galaxies without spiral structure. S/SB: unbarred/barred Sa/b/c: bulge size/ brightness decreases, so does tightness with which arms are wound. Irr: amorphous or disrupted. Question C2(b) The Milky Way is a typical large spiral galaxy. Explain: how you can deduce simply from observations of the night sky (at a suitably dark site) that the Milky Way is a disc galaxy and that the Sun is located fairly close to the plane of the disc; [3] We see a band of stars which cuts the night sky in half This suggests a flattened distribution like a disc (see diagram) if MW were a flattened elliptical, band would be less well defined if we were out of the plane, band would be broader and less symmetrical why we think that the mass of the Milky Way is dominated by dark matter, rather than by stars; [3] Rotation curve of galaxy is flat out to large distances, and value is larger than expected from the summed masses of all stars therefore most of the mass is not seen as luminous stars, and is also more spread out than the stars are Question C2(b) The Milky Way is a typical large spiral galaxy. Explain: the evidence for the presence of a supermassive black hole at the centre of the Milky Way galaxy. [3] Stars near the Galactic centre can be seen in infra-red light. [0.5] They are observed to orbit the Galaxy’s centre of mass on timescales of a few years. Newton’s laws can thus be used to calculate the mass they are orbiting, which turns out to be ~3 million solar masses. [1.5] This mass is confined within a volume smaller than the solar system (from the orbits and evidence of sudden flares in x-ray and radio). Therefore it must be a black hole (anything else of this mass would be much larger) [1]