Answers to problem sheet

Total of 62 marks
21.7 = 35 % (pass mark for an elective module)
24.8 = 40 %, 31 = 50 %, 37.2 = 60 %, 43.4 = 70 %, 49.6 = 80 %, 55.8 = 90 %
I give bonus marks. Add them in to the standard mark to get the total.

1. nuclear fusion (1). 4H -> 4He+energy (1)
2. Any material where the photons interact many times with the electrons before escaping. (1) so it does not depend on chemical composition (1)
3. They are the same (1)
4. plot a spectrum - intensity of light versus its wavelength. The spectrum peaks at a wavelength which is uniquely related to temperature. (1). a hot object would have a spectrum which peaks at a shorter wavelength than a cool one. (1)
5. no, photons interact many times with electrons before they can escape, so it takes them a long time to get out from the center of the sun (1)
6. neutrinos produced in the core of the sun can travel freely out as they do not interact easily with anything! (1)
7. protons and neutrons are located in the nucleus, with the electrons orbiting around. (1) The electrons can only be found at specific energy levels in the atom (1)
8. The electron can absorb a photon if its energy is exactly equal to the energy difference between its current energy level and a higher energy level in the atom. (1) The electron can then drop back down to a lower energy by emitting a photon whose energy is the same as the difference in energy levels.(1)
9. 1 mark for shape, 1 mark for temperature, 1 mark for OBAFGKM
10. identical stars so they have the same absolute luminosity. Their apparent brightness is determined by the inverse square law. star A is 3x further away so is 9x fainter. so star B is the brighter, by 9x. (1)
11. EITHER
trigonometric parallax. measuring the small shift in position of a nearby star with respect to further stars as the Earth moves around the sun. (1)
OR
spectroscopic parallax. Measure the spectrum of a star, and so classify it on the HR diagram. Then since we know its absolue luminosity we can get the distance via the inverse square law (1)
12. The wavelength of light emitted by a moving object is shifted (1)
13. The doppler shift gives velocity in the line of sight (1) and direction of motion (1)
14. star B moves fastest (1) and is comming towards us (1)
15. B produces the largest shifting of the spectral lines (1) It has the maximum velocity along our line of sight and the doppler shift can only tell us about velocities along the line of sight (1)
16. star A is more massive as it moves more slowly (1)
17. mass (1). Stars balance gravity pulling in with the thermal pressure pushing outwards. Higher mass means higher gravity so it must have a higher temperature to balance this, and so moves to the left on an HR diagram. At higher temperatures all the nuclear reactions go very much faster so the luminosity is higher (moving it up on the HR diagram). (1)
18. Massive stars have higher temperatures in order to balance gravity. At higher temperatures all the nuclear reactions go VERY much faster so the luminosity is VERY much higher. Stellar lifetime is total Energy/luminosity. For massive stars the total energy goes up with the mass but the luminosity goes up much more so the lifetime is shorter. (1)
19. core of a main sequence star has nuclear fusion converting Hydrogen-Helium+energy (1). It is stable because it balances gravity pulling in against the thermal pressure of the hot gas pushing out. (1) If a star core produced more energy then the temperature would go up so the thermal pressure would go up so the core would expand. (1) If the star core produced less energy then the thermal pressure goes down and the core contracts. (1)
20. 1 mark for the protostar collapse, 1 mark for red giant branch, 1 mark for the planetary nebula/white dwarf branch. Sun's main sequence lifetime is 10 thousand million years. (1)
21. 1 mark for the protostar collapse, 1 mark for supergiant branch, 1 mark for the supernovae explosion.
22. 1 mark for protostar collapse, 1 mark for evolution to a white dwarf.
23. most mass is lost when a star is highly evolved either in supernovae explosions (1) or planetary nebulae formation (1)
24. a planetary nebula forms from a red giant - the outer layers of the atmosphere are so far away that the gravity holding them to the core is quite weak and they can be blown away (1). The core forms a white dwarf. (1) Stars from about 0.4-6x the mass of the sun will eventually form planetary nebulae. (1)
25. Supernovae happen when a massive star has an iron core core which becomes so big that its gravity is stronger than can be held by electron degeneracy pressure (1) They can also happen when a formerly stable white dwarf or neutron star gains enough material from a binary companion to push it over the limit where degeracy pressure can hold it up against gravity (1)
26. The chemical elements up to iron are built up by nuclear fusion reactions in heavy stars (1). These are then scattered into interstellar space by supernovae explosions (which also produce elements heavier than iron). This enriches the abundances of heavy elements in any nearby clouds of gas and dust, and the shock wave from the supernovae can also trigger these clouds to collapse into new stars. The heavy elements seen on Earth (and in the rest of the solar system) must have come form a previous supernova explosion (1)
27. Fusing iron to build heavier nuclei does not release any more energy - in fact it TAKES some. (1) Elements heavier than iron are produced in the explosive conditions of a supernova (1)
28. Light ALWAYS travles at the speed of light, irrespective of the motion of the observer (Einstein's special relativity). So the space traveller sees the light from her headlamps travelling at the speed of light, as do we (1)
29. A white dwarf holds itself up against gravity by electron degeneracy pressure - a quantum mechanical effect of electrons not liking to be squashed in a box (1). The electrons move faster to support more mass, and the limit to the mass they can support is when the electrons are moving at close to the speed of light, giving a maximum mass of about 1.4x the mass of the sun. (1) Any one of the following observations give 1 mark: Observe white dwarfs directly in nearby star clusters as hot objects, which are much less luminous than main sequence stars at that temperature because of their small surface area, OR see their gravity affecting a companion star in binary star system to get the mass, coupled with their low luminosity and high temperature, OR see them accrete matter in close binary systems.
30. A neutron star holds itself up against gravity by neutron degeneracy pressure - a quantum mechanical effect of neutrons not liking to be squashed in a box (1). The neutrons move faster to support more mass, and the limit to the mass they can support is when the electrons are moving at close to the speed of light, giving a maximum mass of ~3x the mass of the sun. (1) Pulsars give some of the best evidence for the existance of neutron stars (1)
31. There is no mass limit for black holes (OR the mass of the black hole is limited to be less than the mass of the star which formed it!) (1) There are binary systems which produce intense X-ray emission, and where the unseen companion has a mass which is bigger than 3x the mass of the sun so it cannot be a neutron star. (1)