9.2 Astrophysics - Classification of Stars

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9.2 Astrophysics - Classification of Stars – Questions

Q1. The table summarises some of the properties of four stars in the constellation Hercules.

Spectral Apparent Star Distance/pc class magnitude Kornephoros 43 G 2.8

Rasalgethi 110 M 3.0

Rutilicus 11 G 2.8

Sarin 23 A 3.1

(a) Define the parsec. You may use a diagram as part of your answer.

______

______(2)

(b) Deduce which star is larger, Kornephoros or Rutilicus.

______

______(3)

Page 1 of 45 Calculate the corresponding temperature for this curve.

temperature = ______K (2)

(d) Explain which star produced the black-body radiation curve described in question (c).

______

______(2)

(e) Which star has the brightest absolute magnitude?

Tick (✔) the correct box.

Kornephoros

Rasalgethi

Rutilicus

Sarin

(1)

(f) Determine the absolute magnitude of Sarin.

absolute magnitude = ______(3) (Total 13 marks)

Q2. Menkalinan is an eclipsing binary star system in the constellation of Auriga. Figure 1 shows the variation in apparent magnitude with time (light curve) for Menkalinan.

Page 2 of 45 Figure 1

Analysis of the spectrum of one of the stars shows a periodic variation in wavelength. Figure 2 shows the results for one of the spectral lines in the Hydrogen Balmer series. The wavelength for this line as measured for a source in a laboratory on the Earth is 656.28 nm.

Figure 2

(a) Describe the physical processes that give rise to the shape of each graph. Go on to show how the information in the graphs can be used to determine properties, such as the speed and period, of the Menkalinan binary system. You should include appropriate calculations in your answer.

The quality of your written communication will be assessed in your answer. (6)

(b) The black body temperature of each star is approximately 9200 K.

Explain why a Hydrogen Balmer line was chosen for the analysis of wavelength

Page 3 of 45 variation.

______

______(2)

Calculate the value of the absolute magnitude of Menkalinan when it appears dimmest.

absolute magnitude = ______(3) (Total 11 marks)

Q3. (a) Explain what is meant by

apparent magnitude

______

absolute magnitude

______

______(2)

(b) (i) The star Betelgeuse has a mean apparent magnitude of +0.5 and an absolute magnitude of –5.7. Use the definitions you have given above to deduce (without calculation) that the distance between Betelgeuse and Earth is greater than 10 pc.

______

Page 4 of 45 ______

______

(ii) The star Proxima is much closer to Earth than 10 pc and its mean apparent magnitude is +11.0. Giving a reason, suggest a value for its absolute magnitude.

______

(iii) Using the values of apparent magnitude and absolute magnitude from part (b) (ii), determine the distance, in pc, between Proxima and Earth.

______

______(6) (Total 8 marks)

Q4. The table has information on two stars.

Apparent Absolute Spectral Star magnitude magnitude class Sirius –1.4 –1.4 A

Rigel 0.12 –7.1 B

(a) State the difference between apparent magnitude and absolute magnitude.

______

______(2)

(b) Sirius has an intensity of 1.18 × 10–7 Wm–2 at the Earth. The distance between Sirius and the Earth is 8.13 × 1013 km.

Calculate the luminosity of Sirius. Give an appropriate unit for your answer.

Page 5 of 45 luminosity ______unit ______(3)

______

______(2) (Total 7 marks)

Q5. (a) Draw a ray diagram for an astronomical refracting telescope in normal adjustment. Your diagram should show the paths of three non−axial rays through both lenses.

Label the principal foci of the two lenses.

(2)

(b) Most modern optical observatories make use of reflecting telescopes rather than refracting telescopes.

Discuss the principal optical advantages of reflecting telescopes.

______

Page 6 of 45 ______

______

______(4)

(c) The Greek astronomer Hipparcos used naked-eye observations to develop a scale for comparing the apparent magnitude of stars.

Explain what is meant by apparent magnitude and describe the main features of the Hipparcos scale.

______

______(6) (Total 12 marks)

Page 7 of 45 Q6. The Summer Triangle consists of three stars, Altair, Deneb and Vega. Some of the properties of the three stars are summarised in the table below.

Altair Deneb Vega

surface 7700 8500 9600 temperature / K

apparent magnitude 0.77 1.25 0.03

absolute magnitude 2.21 –8.38 0.60

(a) The three stars belong to the same spectral class.

State and explain which spectral class they belong to.

______

______(2)

(b) Deduce which of the three stars appears brightest.

______

______(2)

distance = ______pc (3)

(d) Deduce which of the three stars is the largest.

______

Page 8 of 45 ______

______

______(3)

(e) Calculate the wavelength of the peak in the black body radiation curve of Altair.

wavelength = ______m (2) (Total 12 marks)

Q7. (a) The table summarises some of the properties of two stars in the constellation of Ursa Minor.

apparent radius of star spectral name magnitude radius of the Sun class

Polaris 2.0 50 F

Kocab 2.0 50 K

(i) Using these data, describe and explain one similarity and one difference in the appearance of the two stars as seen with the unaided eye by an observer on the Earth.

similarity______

______

difference______

______

______(2)

Page 9 of 45 (ii) Deduce which of the two stars is further from the Earth.

______

______(3)

(b) Ursa Minor also contains the galaxy NGC 6251. Measurements indicate that the light from the galaxy has a red shift, z, of 0.025 and that the galaxy is 340 million light years from Earth.

(i) Use these data to calculate a value for the Hubble constant.

value ______k ms–1 Mpc–1 (3)

(ii) Use your answer to part (b)(i) to estimate a value for the age of the Universe. State an appropriate unit for your answer.

age ______unit ______(3) (Total 11 marks)

Q8. (a) Define the term absolute magnitude.

______

______(1)

(b) The figure below shows the axes of a Hertzsprung-Russell diagram.

Mark suitable scales on the absolute magnitude and temperature axes.

Page 10 of 45

temperature / K (2)

(i) the Sun (1)

(ii) star W, which has the same intrinsic brightness as the Sun, but has a significantly higher temperature (1)

(iii) star X, which has a similar spectrum to the Sun, but is significantly larger (1)

(iv) star Y, which is significantly larger than the Sun and has prominent absorption lines of neutral atoms and titanium oxide (TiO) in its spectrum. (1)

(d) How does the diameter of star W, in part (ii), compare with the diameter of the Sun? Explain your answer.

______

Page 11 of 45 ______(3) (Total 10 marks)

Q9. (a) Define the absolute magnitude of a star.

______

______(1)

(b) The figure below shows the axes of a Hertzsprung-Russell (H-R) diagram.

(i) On each axis indicate a suitable range of values.

(ii) Label with an S the current position of the Sun on the H-R diagram.

(iii) Label the positions of the following stars on the H-R diagram:

(1) star W, which is significantly hotter and brighter than the Sun,

(2) star X, which is significantly cooler and larger than the Sun,

(3) star Y, which is the same size as the Sun, but significantly cooler,

(4) star Z, which is much smaller than the Sun, and has molecular bands as an important feature in its spectrum. (7) (Total 8 marks)

Q10. Treated as a single source, the Andromeda galaxy has an apparent magnitude of 3.54 and an absolute magnitude of –20.62.

(a) Calculate the distance to the Andromeda galaxy.

Page 12 of 45 ______

______

______(2)

(b) The Andromeda galaxy is believed to be approaching the Milky Way at a speed of 105 km s–1. Calculate the wavelength of the radio waves produced by atomic hydrogen which would be detected from a source approaching the observer at a speed of 105 km s–1.

wavelength of atomic hydrogen measured in a laboratory = 0.21121 m.

______

______(2)

(c) Some astronomers believe the Andromeda galaxy may collide with the Milky Way in the distant future. Estimate a time, in s, which will elapse before a possible impact with the Milky Way.

______

______(2) (Total 6 marks)

Q11. (a) Bellatrix and Betelgeuse are stars in the constellation of Orion. Some of their properties are summarised below.

Bellatrix Betelgeuse

absolute magnitude –6.0 –2.7

apparent magnitude 0.4 1.6

black-body temperature / K 22 000 2 400

(i) Explain what is meant by absolute magnitude.

Page 13 of 45 ______

______

______(1)

(ii) Which of the two stars is closer to the Earth? Explain your answer.

______

______(1)

(b) (i) Calculate the wavelength of the peak intensity in the black-body radiation curve of Bellatrix.

answer = ______m (2)

(ii) Sketch the black-body radiation curve for Bellatrix. Label the wavelength axis with a suitable scale.

(3)

Page 14 of 45 (c) Detailed analysis of the light from both stars reveals the presence of prominent absorption lines in the spectra.

(i) To which spectral class does Bellatrix belong?

______(1)

(ii) Prominent features in the Bellatrix spectrum are the Balmer absorption lines due to hydrogen. State the other element responsible for the prominent absorption lines in the spectrum of Bellatrix.

______(1)

(iii) Why does the spectrum of Betelgeuse not contain prominent Hydrogen Balmer absorption lines?

______

______(1) (Total 10 marks)

Q12. Sirius is a binary system consisting of two stars, Sirius A and Sirius B, the properties of which are summarised below.

Sirius A Sirius B absolute magnitude 1.4 11.2 apparent magnitude –1.4 8.4 diameter / 103 km 2400 12 black-body 10 000 25 000 temperature/K

(a) Calculate the distance to Sirius, giving an appropriate unit.

distance = ______(3)

(b) (i) Calculate the ratio

Page 15 of 45

ratio = ______(2)

(ii) Show that data in the table suggests that one star is about 8000 times brighter than the other.

______

______(2)

(iii) With reference to the spectra of the two stars, explain why the value in part b (ii) is much greater than the answer to part b (i).

______

______(3) (Total 10 marks)

Q13. (a) The graph shows the axes of a Hertzsprung–Russell (H–R) diagram.

Page 16 of 45

(i) Label the spectral class axis with a suitable scale. (1)

(ii) Complete the H–R diagram by marking the positions of the main sequence, dwarf star and giant star regions. (2)

(b) The table summarises some of the properties of three stars in the constellation Aries.

Apparent Star Temperature / K Radius / m magnitude Hamal 2.0 4500 1.0 × 1010 Sharatan 2.7 9000 1.8 × 109 41 Arietis 3.6 12000 9.6 × 1010

(i) With reference to the data in the table, compare the three stars. Your answer should include a discussion of:

• the appearance to the naked eye of the three stars as seen from Earth • the spectrum of the three stars • the region of the Hertzsprung–Russell diagram to which each star belongs.

The quality of your written communication will be assessed in your answer. (6)

(ii) Hamal is 66 light years from the Earth. Calculate the absolute magnitude of Hamal.

Page 17 of 45 absolute magnitude = ______(3)

(iii) Identify which star is the greatest distance from Earth. Explain your answer.

______

______(3) (Total 15 marks)

Q14. The table gives information on two stars.

apparent star spectral class distance/pc magnitude

Proxima Centauri 11 M 1.30

Antares 1.0 M 160

(a) (i) Explain what is meant by

apparent magnitude ______

______

absolute magnitude ______

______

(ii) The two stars named in the table are viewed through a telescope. State and explain one difference in the appearance of the two stars.

______

______(4)

(b) (i) Draw a Hertzsprung-Russell diagram for main sequence stars, Giant Stars

Page 18 of 45 and White Dwarfs.

(ii) With reference to the table, calculate the absolute magnitude of Proxima Centauri.

______

(iii) Given that the absolute magnitude of Antares is –5, mark and label with an X its approximate position on the Hertzsprung-Russell diagram. (6)

______

(ii) Hence, deduce which star has the larger diameter. Explain how you arrive at your answer.

______

______(4) (Total 14 marks)

Q15. (a) Define

(i) apparent magnitude,

Page 19 of 45 ______

______

(ii) absolute magnitude.

______

______(2)

(b) Bellatrix and Elinath are two stars with the same apparent magnitude. The distance from the Earth to Bellatrix is 470 light years and its absolute magnitude is –4.2.

(i) Calculate the distance to Bellatrix in parsecs.

______

(ii) Calculate the apparent magnitude of Bellatrix.

______

(iii) Elinath has an absolute magnitude of –3.2. State, giving a reason, which of the two stars is closer to the Earth.

______

______(6) (Total 8 marks)

Q16. (a) The table summarises the properties of five of the stars in the constellation of Cassiopeia.

name absolute apparent spectral magnitude magnitude class

Achird 4.6 3.5 G

Chaph 1.9 2.3 F

Ruchbah 0.24 2.7 A

Page 20 of 45 Segin –2.4 3.4 B

Shedir –0.9 2.2 K

Explaining your answer in each case, state which star

(i) is the hottest,

______

(ii) is likely to appear orange in colour,

______

(iii) appears the brightest from Earth,

______

(iv) is less than 10 pc away from the Earth.

______

______(4)

(b) The constellation Cassiopeia contains another star with an apparent magnitude of 2.2, absolute magnitude of –4.6 and a surface temperature of 12 000 K. Calculate, for this star,

(i) its distance from the Earth,

______

(ii) the peak wavelength in its black body radiation curve.

______

Page 21 of 45 ______(3) (Total 7 marks)

Q17. In 1999 a planet was discovered orbiting a star in the constellation of Pegasus.

(a) State one reason why it is difficult to make a direct observation of this planet.

______

______(1)

(b) The initial discovery of the planet was made using the radial velocity method which involved measuring a Doppler shift in the spectrum of the star.

Explain how an orbiting planet causes a Doppler shift in the spectrum of a star.

______

______(2)

Explain how an orbiting planet causes a change in the apparent magnitude of a star. Sketch a graph of apparent magnitude against time (a light curve) as part of your answer.

______

______(3) (Total 6 marks)

Page 22 of 45 Q18. The Earth’s atmosphere absorbs electromagnetic radiation of certain wavelengths. Detectors on the surface of the Earth are largely restricted to the visible and radio regions.

(a) (i) On the axes below, draw the black body radiation curve for the Sun.

(ii) Mark on the wavelength axis the region affected by the atmosphere’s absorption of ultra violet radiation.

(iii) What is responsible for this absorption?

______

(iv) What effect can this absorption have on the measured temperature of a star? Explain your answer.

______

______(4)

(b) The atmosphere has little effect on radio waves between 30 MHz and 300 GHz. This radio window was first exploited in 1946 when a short pulse of radio waves of wavelength 2.7 m was transmitted from the Earth and reflected back by the Moon.

(i) Show that the frequency of the transmitted waves falls within the radio window.

______

(ii) The experimenters had to take into account the relative movement of the

Page 23 of 45 Earth and Moon when tuning the receiver. The maximum difference between the frequency of the detected and transmitted waves was 300 Hz.

What is the name of this effect?

______

(iii) Calculate the relative velocity of the Earth and Moon when the frequency of the received signal was 300 Hz greater than the transmitted frequency.

______

______(5) (Total 9 marks)

Q19. (a) The graph shows part of the visible region of the spectrum of the star Vega.

The absorption lines are due to excited hydrogen atoms. The wavelength of each absorption is given in nm.

You may be awarded marks for the quality of the written communication provided in your answer.

(i) Explain how hydrogen atoms produce these absorption lines.

______

(ii) The diagram below shows the first six energy levels of a hydrogen atom. Draw an arrow to show the largest energy transition which produces an absorption line in the visible spectrum of Vega.

Page 24 of 45

(iii) State the value of the wavelength corresponding to this transition.

______

(iv) What is the name given to the series which gives rise to the visible region of the hydrogen spectrum?

______

(v) For which spectral classes are these lines the dominant feature?

______(4)

(b) (i) The wavelength at maximum intensity in the spectrum of Vega has a value of 300 nm. Show that this corresponds to a value of about 10 000 K for the surface temperature of Vega.

______

(ii) State the assumption made in your answer to (b)(i).

______(2)

______

______(1) (Total 7 marks)

Q20. Figure 1 shows the black body radiation curves for three stars, labelled P, Q and R.

Page 25 of 45

Figure 1

(a) (i) State and explain, without calculation, which one of the three stars is the hottest.

______

(ii) Calculate the black body temperature of the hottest star.

______

______(3)

(b) More detailed analysis of the hottest star’s spectrum revealed the presence of Hydrogen Balmer absorption lines.

(i) For which two spectral classes are these lines the prominent feature?

______

(ii) Describe how these absorption lines are produced in the spectrum of a star.

______

Page 26 of 45 ______

______

______(4) (Total 7 marks)

Q21.

(a) Using the axes below, sketch the emissive power of a black body, Eλ, as a function of wavelength for each of three temperatures, 1000K, 1200K and 1600K. Indicate the temperature on each curve.

(b) (i) Wien’s displacement law may be written as λmaxT = constant. State what λmax represents.

______

(ii) Obtain the value of the constant from the Data booklet and calculate λmax for a temperature of 1600K.

______

(iii) Assuming that λmax for the Sun lies within the range of the visible spectrum, use Wien’s law to estimate the temperature of the Sun.

______

Page 27 of 45 ______(5)

(c) Stefan’s law for a black body may be written as E = σT4 where E, the energy radiated per second per square metre of the surface area, has units W m–2.

(i) Hence state how a value of E may be obtained from one of the curves drawn in part (a) for a given temperature.

______

(ii) For a black body of surface area A, give Stefan’s law in the form which gives total radiative power of the body.

______(2)

(d) (i) The diagram represents the Earth in orbit around the Sun. Given that the Earth receives 1400 W m–2 of energy from the Sun and that the Sun emits energy equally in all directions, estimate the total output power, in W, of the Sun.

mean radius, R, of the Earth’s orbit around the Sun = 1.5 × 1011 m

______

(ii) Hence, use Stefan’s law to deduce the temperature of the Sun.

radius of the Sun = 7.0 × 108 m

______

______(4)

Page 28 of 45 (Total 14 marks)

Q22. The table compares two properties of the Sun with Arcturus, a star in the constellation Bootes.

Sun Arcturus

surface temperature/K 6 000 5 000

absolute magnitude 5 0

(a) (i) Assuming the Sun acts as a black body, calculate the wavelength at which maximum emission occurs in its spectrum.

______

(ii) The graph shows the black body radiation curve for the Sun. Use your answer to (i) to enter values on the wavelength axis in the 4 places provided.

(iii) Without calculation, sketch on the axes above a black body curve for Arcturus. (4)

(b) (i) Explain how the information in the table indicates that Arcturus is 100 times brighter than the Sun.

______

(ii) Assuming that the power output of Arcturus is 100 times greater than that of the Sun, show that its surface area must be approximately 200 times greater.

______

Page 29 of 45 ______

______(4) (Total 8 marks)

Q23. (a) Wien’s displacement law for black body radiation is given by

λmaxT = constant.

State the meaning in this equation of λmax.

______

______(1)

(b) The black body radiation curve for a certain star is shown in Figure 1.

Figure 1

Calculate the temperature of the star, given that the Wien constant is 2.9 × 10–3 m K.

______

______(2)

(c) Figure 2 shows the effect on the radiation from the star of a cloud layer that does not absorb the light evenly at all wavelengths.

Page 30 of 45

Figure 2

(i) State the range of wavelengths absorbed most strongly by the cloud.

______

(ii) Explain why this absorbing cloud alters the estimate of the temperature of the star. Would the new estimated temperature be greater or less than the original temperature?

______

______(3) (Total 6 marks)

Q24. (a) (i) On the axes below draw the Hertzsprung-Russell (H-R) diagram labelling the main sequence stars, dwarf stars and giant stars. Complete the horizontal axis by labelling the spectral classes.

Page 31 of 45

(ii) On the H-R diagram, mark with an X the current position of the Sun and draw a line to represent the evolution of the Sun, from its formation to its eventual state as a white dwarf. (4)

(b) Matar is a star in the same spectral class as the Sun.

(i) State two properties common to Matar and the Sun.

______

(ii) The distance to Matar is 330 light years. What is this distance in parsec?

______

(iii) The apparent magnitude of Matar is 2.9. Calculate its absolute magnitude.

______

(iv) Which is the larger star, Matar or the Sun? Explain your answer.

______

Page 32 of 45 ______(6) (Total 10 marks)

Q25. (a) Explain what is meant by light year and parsec.

(i) light year

______

(ii) parsec

______

______(2)

(b) 95 Herculis is approximately 450 light years from the Earth. It is a binary system consisting of two stars each of apparent magnitude 5.1. One star belongs to spectral class A and the other to spectral class G.

(i) Calculate the absolute magnitude of either of the stars of 95 Herculis.

______

(ii) To which spectral class does the hotter star belong? Justify your answer.

______

(iii) To which spectral class does the smaller star belong? Justify your answer. (5)

(c) The two stars of 95 Herculis are separated by an angle of 1.8 × 10–3 degrees. Calculate the minimum diameter of an aperture which would just allow these stars to be resolved wavelength of the light = 5.0 × 10–7 m

______

______(2) (Total 9 marks)

Page 33 of 45 Q26. The graph shows the variation of intensity with wavelength for the star 40 Eridani B.

(a) (i) Calculate the black body temperature of 40 Eridani B.

State an appropriate unit for your answer.

temperature = ______unit ______(3)

(ii) 40 Eridani B has a total power output of 4.2 × 1024 W.

Calculate its radius.

radius = ______m (2)

(b) (i) Which of the following regions of the Hertzsprung-Russell diagram does 40 Eridani B belong to?

Page 34 of 45 Tick (✓) the correct answer.

main

sequence

dwarf star

giant star

(1)

(ii) Give reasons for your answer to part (i).

______

______(2) (Total 8 marks)

Q27. Antares is a red supergiant star in the constellation of Scorpio. It has a mass about 18 times that of the Sun. Eventually the star will become a supernova, leaving behind a core that could form a neutron star or a black hole.

(a) State what is meant by a supernova.

______

______(1)

(b) State the defining properties of a neutron star.

______

______(2)

Calculate the Schwarzschild radius of a black hole with a mass twice that of the Sun.

Page 35 of 45

radius = ______m (2)

(d) Some scientists are concerned about the consequences for the Earth of a supernova occurring in a nearby part of the galaxy.

Explain the cause of this concern.

______

______(2) (Total 7 marks)

Q28. There is a supermassive black hole at the centre of the Milky Way galaxy. It is difficult to resolve images of the region around this black hole directly.

(a) (i) Sketch, on the axes, the variation in intensity of the diffraction pattern produced when light from a point object passes through a circular aperture.

(2)

(ii) The Rayleigh criterion is used to determine the smallest angular separation between two point objects which can be resolved by a telescope. With reference to the diffraction patterns formed, explain what is meant by the Rayleigh criterion. You may draw a diagram to aid your explanation.

Page 36 of 45

______

______(2)

(b) The supermassive black hole at the centre of the Milky Way galaxy has a mass equal to 4.1 million solar masses. Calculate the Schwarzschild radius, Rs, for this black hole. Give your answer to an appropriate number of significant figures.

Rs ______m (3)

(c) Astronomers investigating the supermassive black hole at the centre of the Milky Way galaxy detect radio waves at a frequency of 230 GHz. By correlating the information from several radio telescopes, they can obtain images with the same resolution as a single radio telescope with a diameter of 5000 km.

(i) Calculate the minimum angular separation which could be resolved by a radio telescope of diameter 5000 km detecting waves of frequency 230 GHz.

angular separation ______rad (2)

(ii) The centre of the Milky Way galaxy is 25 000 light years from the Earth.

Show that the limit of the resolution of the telescope is approximately five times the angle subtended by the Schwarzschild radius of the black hole at this distance.

Page 37 of 45

(2) (Total 11 marks)

Q29. NGC 3842 is a galaxy which contains one of the biggest black holes ever discovered.

(a) State what is meant by a black hole.

______

______(1)

(b) The mass of the black hole in NGC 3842 is believed to be 1.0 × 1010 times greater than that of the Sun.

Calculate the radius of its event horizon.

radius = ______m (2)

Estimate, using these data, an age in seconds for the Universe.

age of Universe = ______s (3) (Total 6 marks)

Q30. (a) Sketch, on the axes, the light curve for a typical type 1a supernova.

Page 38 of 45 Label the axes with suitable scales.

(3)

(b) Type 1a supernovae can be used as standard candles.

Explain what is meant by a standard candle.

______

______(1)

Describe this controversy and how the measurements led to it.

______

Page 39 of 45 (3) (Total 7 marks)

Q31. In 2013 a gamma-ray burst was detected from a region of space between the constellations of Leo and Ursa Major.

(a) State the event that was the likely cause of this gamma−ray burst.

______

______(1)

(b) Measurements of the optical remnant of the event revealed an object with a red shift z of 0.34.

Calculate, ignoring relativistic effects, the distance to this object in light year. Give your answer to an appropriate number of significant figures.

distance = ______light year (4)

(c) The total energy of the gamma−ray burst was estimated to be 1047 J. Many scientists are concerned that a gamma-ray burst in the direction of the Earth could cause major problems.

Show that this is similar to the energy that would be released if the mass of the Sun were all converted to energy. (2) (Total 7 marks)

Q32. (a) Betelgeuse is a red supergiant star with a mass approximately ten times greater than that of the Sun. Eventually it is quite likely that Betelgeuse will become a supernova, leaving a neutron star or perhaps a black hole.

State a significant property of a

(i) supernova,

______

(ii) neutron star,

Page 40 of 45 ______

______

(iii) black hole.

______

______(3)

(b) Calculate the Schwarzchild radius for a black hole whose mass is ten times greater than that of the Sun.

______

______(2) (Total 5 marks)

Q33. The Antennae Galaxies are a pair of colliding galaxies in the constellation Corvus.

(a) Measurements of the red shift of radio signals from the galaxies suggest they are approximately 25 Mpc from the Earth.

(i) Explain what is meant by red shift.

______

______(1))

(ii) Calculate the recessive velocity of the Antennae Galaxies.

answer = ______km s–1 (2)

(b) SN 2008sr was a type 1a supernova detected in the Antennae Galaxies. The figure below is the light curve of a type 1a supernova.

Page 41 of 45

(i) With reference to the figure above, explain why type 1a supernovae can be used as standard candles to determine distances.

______

______(2)

(ii) The peak value for the apparent magnitude of this supernova was 12.9. Using this measurement and information from the figure above, calculate the distance to the Antennae Galaxies in Mpc.

Page 42 of 45

answer = ______Mpc (2)

______

______(1) (Total 8 marks)

Q34. (a) Sketch a Hertzsprung-Russell diagram using the axes below. Label the approximate positions of main sequence stars, Red Giant stars, White Dwarf stars and the Sun.

(3)

(b) The evolution of a star from the main sequence depends on its mass. A certain star in the main sequence, in a position close to the Sun, evolves into a Red Giant.

(i) Compare the brightness of this star when it is a Red Giant to when it was in the main sequence.

______

(ii) Given that the hydrogen in this star undergoes fusion, suggest a sequence of events which causes this star to evolve into a Red Giant.

______

Page 43 of 45 ______

______

______(4)

(i) What property of this star causes it to be a black hole? Explain why it is so named.

______

(ii) State what is meant by the term event horizon and calculate the radius of the event horizon for this star, using data from the Data booklet.

______

______(5) (Total 12 marks)

Q35. Centaurus A is the nearest example of an active galactic nucleus. Many astronomers believe a supermassive black hole at the centre of such a galaxy produces a quasar as it consumes the material of its nearby stars.

(a) Explain what is meant by the event horizon of a black hole.

______

______(1)

(b) (i) The mass of the black hole is 60 million times the mass of the Sun. Calculate the radius of its event horizon.

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answer = ______m (2)

(ii) Calculate the average density of the matter within its event horizon.

answer = ______kg m–3 (2) (Total 5 marks)

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