Edexcel A2 Physics Questions and answers 7.1.1 Astrophysics and cosmology : From apples to galaxies
(Page-174)
1. Explain why the weight of an object on the Earth is found by multiplying its mass in kilograms by 9.81. The gravitational field strength of Earth is 9.81 N kg-1 at its surface. 2. Calculate the gravitational force between two 0 particles in deep space, if they are 8 metres apart. The mass of a neutral pion is 2.40 x 1028 kg. 6.0 x 10-68 N 3. Calculate the gravitational force between the Earth and the Moon if the Moon’s mass is 7.35 x 1022 kg. 2.0 x 1020 N 4. Calculate the average distance of the Earth from the Sun, if the mass of the Sun is 6 x 1030 kg. 1.5 x 1011 m
7.1.2 Astrophysics and cosmology : Gravitational fields
(Page-177)
1. Calculate the gravitational field strength at the orbit of a polar satellite that travels at 900 km above the surface of the Earth. 7.5 m s-2 2. Compare the magnitudes of the force of attraction between an electron and a proton in a hydrogen atom (radius = 0.25 x 1010 m) with the gravitational attraction of the Sun on Pluto. Pluto has a mass of 1.29 x 1022 kg and orbits at a distance of 5900 million kilometres from the Sun. H atom: F = 3.69 x 10-7 N Pluto: F = 4.94 x 1016 N The solar system force is 1023 times bigger for a system which is 1022 times larger. 3. What would the mass of the Moon have to be for the Earth’s gravity to exert the same force of attraction on it as the electrostatic attraction of the proton for the electron in a hydrogen atom? 1.36 x 10-4 kg 4. There is a point on the line between the centres of the Earth and the Moon where their gravitational fields have equal magnitude but are in opposite directions, effectively creating a point of zero gravity. Calculate the distance of this point from the centre of the Earth. 3.46 x 108 m
Edexcel A2 Physics Questions and answers
7.2.1 Astrophysics and cosmology : Stellar properties
(Page-180)
1. What is the luminosity of the star Sirius, which has a surface temperature of 12,000 K and a diameter of 2,220,000 km? 7.15 x 1028 W 2. a) The Sun’s surface temperature has been measured as 5700 K. Calculate the peak wavelength of the solar spectrum. b) The peak wavelength from the Sun is in fact measured on Earth as being 470 nm. Why is the measured value different from your calculated value from part a? a) 5.08 x 10-7 m
b) Atmospheric absorption
3. Calculate the peak wavelength output we would expect of Bellatrix if its surface temperature is 21,500 K. 1.35 x 10-7 m 4. a) From fig. 7.2.5, calculate the temperatures of Antares and Spica. b) What is the significance of the difference in the area underneath each curve? a) [need to see final aw] b) variation in total energy output 5. a) Stars Ori and Cet have temperatures of approximately 11 000 K and 3600 K respectively. Calculate the wavelength at which the intensity of radiation from each star is a maximum. Give your answers in nanometres. b) Use the Stefan-Boltzmann law to calculate the power emitted per square metre of surface, measured in W m–2, for Ori. c) The power emitted per square metre of surface for Cet = 1.0 × 107 W m–2. Copy the axes below and sketch two graphs, showing how this emitted power is distributed over different wavelengths for each star. Label your graphs Ori and Cet. Relative emitted power
0
200
400
600
visible
800 1000 1200 Wavelength/nm
d) The visible spectrum extends from approximately 400 nm to 700 nm. Use your graphs to explain why Ori is a bluish star, while Cet is reddish.
Edexcel A2 Physics Questions and answers a) β Ori = 260 nm (263 nm) α Cet = 810 nm (805 nm, 800 nm) b) 8.3 × 108 W m–2 c) β Ori peak at ~ 260 nm [e.c.f. their value] [Obviously to left of 400 nm], α Cet peak at ~ 800 nm [e.c.f.] [Obviously to right of 700 nm] also, Area β Ori » area α Cet. d) β Ori at blue end of spectrum; α Cet at red end, BOTH outside visible region
7.2.2 Astrophysics and cosmology : Classifying stars
(Page-186)
1. The mass of the Sun is 6 x 1030 kg. If we assume that it is entirely composed of protons, how many protons is this? If the Sun fuses all its protons over the course of its estimated nine billion year lifetime, how many protons are undergoing nuclear fusion every second? 1.2 x 1057 protons; 4.22 x 1039 protons fuse per second 2. Draw a flow chart showing the life cycles of: a) a star that starts out with six times the mass of the Sun b) a star that starts out with twice the mass of the Sun. a) b) as per fig 7.2.8 3. Calculate the gravitational field strength at the surface of a black hole, if it has five times the mass of the Sun and a diameter of 10 cm. How does this compare to the Earth’s gravitational field strength? 6.67 x 1022 m s-2 4. a) From memory, make a quick sketch of the Hertzsprung–Russell diagram and mark on the path taken by a star with the same mass as our Sun, as it develops through the various stages of its life cycle. b) Mark on your sketch the life cycle path taken by a blue supergiant if it starts out with a mass 8 times that of the Sun. a) As per fig 7.2.10 b) Starts at the top middle of the diagram; moves slightly right; then supernova and neutron stars/black holes are not plotted on the diagram. 5. Why do the nuclear fusion processes within stars tend to produce elements with a mass number that is a multiple of four, such as carbon-12, oxygen-16 and silicon-20? He-4 has an unusually high BE/nucleon and so is a very stable nucleus. Thus multiples of this are also very stable. 6. a) Why can’t the nuclear fusion in stars produce elements higher in the periodic table than iron-56? b) How then do heavier elements than iron-56 exist, when the Big Bang produced an initial Universe composed of only hydrogen and helium? a) To fuse above Iron-56 would involve a drop in BE/nucleon and so would need energy to be put in. b) In a supernova explosion energy is available to fuse nuclei to higher masses than 56. 7. a) When a star moves off the main sequence It initially becomes a red giant. Describe the processes occurring which result in it becoming “giant-sized”. You may be awarded a mark for the clarity of your answer. b) Use Wien’s law to explain why these giant stars look red compared with their appearance when they were on the main sequence. c) Use Stefan’s law to explain why a red giant has greater luminosity than when it was a main sequence star.
Edexcel A2 Physics Questions and answers
7.3.1 Hubble’s law : Distances to the stars
(Page-191)
1. How far away is Alpha Centauri in parsecs? 1.32 pc 2. The parallax angle to Barnard’s Star is 0.545′′. How far away is Barnard’s Star in a) metres b) light years c) parsecs d) astronomical units? a) 1.14 x 1017 m b) 12 ly c) 3.68 pc d) 7.56 x 105 AU 3. The luminosity of Rigel is 3.9 x 1031 W. At the Earth, Rigel’s radiant energy flux is 5.42 x 108 W. How far away is the star? 7.57 x 1018 m 4. Explain why we must know a star’s luminosity in order to determine its distance if it is more than 200 pc away. Why is this more complicated than just looking at how bright the star is in the sky? Trigonometric parallax is not reliable at more than 200 pc. Luminosity decreases with distance; or luminosity can vary over time with some stars. 5. Jupiter’s orbit is 5.2 AU from the Sun. If Jupiter is considered as a black body with a temperature of 110 K, and radius 69900 km, calculate: a) the maximum radiant energy flux at the surface of the Earth due to Jupiter’s electromagnetic emissions (Hint: you will first need to calculate the luminosity) b) the peak wavelength of Jupiter’s energy output. c) How does the energy we receive from Jupiter compare with that we get from the Sun? a) 1.02 x 10-7 W m-2 b) 2.63 x 10-5 m c) much less energy, at generally longer wavelengths 7.3.2 Hubble’s law : The age of the Universe
(Page-194)
1. The galaxy NGC 7320C has a red shift value of z = 0.02. a) At what wavelength would you expect to find the hydrogen alpha line in the spectrum of light from NGC 7320C? b) Use the best modern value for Hubble’s constant to calculate the distance to NGC 7320C in megaparsecs. a) 669.411 nm b) 84.5 Mpc 2. The value for the Hubble constant has varied over the years, from 50 km s1 Mpc1 to 100 km s1 Mpc1, as different star data were used to draw the graph. Calculate the range of ages of the Universe that this represents. 10 – 20 Gyr 3. Use the data shown in fig. 7.3.11 to answer these questions. a) Calculate the recession velocity of each galaxy. b) What would be the rest wavelength for a CIV spectral line? c) What would be the frequency of the SiIV spectral line in galaxy i)? a) [need to see final aw] 4. Hubble’s law can be represented by the formula v = Hd. a) State the unit of the Hubble constant H. b) Show how the age of the Universe can be estimated by using the above formula. State an assumption that has to be made.
Edexcel A2 Physics Questions and answers a) s–1 / km s–1 kpc–1 /km s–1 Mpc–1 b) t = 1/H [Substitute value of H to obtain t]. Assuming since the start of time all galaxies are travelling at constant speed, and there are no gravitational attractive forces. Assuming that the Universe expands at a constant rate.
7.3.3 Hubble’s law : The fate of the Universe
(Page-197)
1. a) What is meant by the Doppler effect (electromagnetic Doppler effect) when applied to light? b) Edwin Hubble reached a number of conclusions as a result of observations and measurements of red-shift. State two of these conclusions. c) The diagram gives values of wavelength for part of the electromagnetic spectrum. Wavelength/ 10–9 m 200 300
UV
400
500
Visible
600
700
IR
A very hot distant galaxy emits violet light just at the edge of the visible spectrum. Estimate the maximum velocity the galaxy could have so that visible light could still be detected as it moves away from the Earth. d) The fate of the Universe is dependent on the average mass-energy density of the Universe. What is meant by the critical density of the Universe?
a) A change in the frequency/wavelength (of the light/radiation from a source) because of relative motion between source and observer. b) (Recession) velocity proportional to galaxy distance [NOT stars]. Red shift due to a galaxy moving away from Earth/observer. Deduction of the expanding Universe [not the Big Bang] c) Maximum velocity = 2.1 × 108 m s–1 d) Density is large enough to prevent Universe expanding for ever but not too big to cause a collapse/contraction of the Universe.
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