9.3 Astrophysics - Hertzsprung-Russel Diagram – Qs

Q1. (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.

(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.

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

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

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Page 1 of 15 (iv) Which is the larger star, Matar or the Sun? Explain your answer.

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______(6) (Total 10 marks)

Q2. 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 ______

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absolute magnitude ______

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(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.

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

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

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(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)

(c) (i) Giving your reason, what can you say about the surface temperature of the two stars?

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

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______(4) (Total 14 marks)

Q3. (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.

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(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.

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(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.

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(c) Nova Muscae is believed to be a black hole with a mass approximately three times that of the Sun.

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

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(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.

Page 4 of 15 ______

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______(5) (Total 12 marks)

Q4. A Hertzsprung-Russell diagram for Main Sequence stars is shown below.

(a) (i) Label on the diagram the regions occupied by White Dwarfs and Red Giants.

(ii) Use the diagram to explain why Red Giant stars must be very much larger than White Dwarfs.

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(b) (i) Mark the spectral classes O to M on the diagram.

(ii) Describe briefly the spectra of stars in class O, class A and class M.

class O ______

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Page 5 of 15 class A ______

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class M ______

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______(6) (Total 10 marks)

Q5. (a) Sketch a Hertzsprung−Russell diagram on the axes on the graph below. Label the position of the main sequence, white dwarf and giant stars.

(3)

(b) Label the minimum and maximum values on the scale of each axis. (2)

(c) Some of the properties of three stars are shown in the table below.

Omicron 2 Rigel Regulus A Eridani distance/light 860 16.5 79 year

apparent 0.13 9.5 1.3 magnitude

Page 6 of 15 temperature/K 12 000 16 500 12 500

Identify the spectral class to which all three stars belong.

Tick (✔) the correct answer in the right hand column.

✔ if correct

A

B

F

G

K

M

O (1)

(d) Explain your answer to part (c).

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(e) The three stars belong to different parts of the Hertzsprung−Russell diagram.

Deduce which star is a white dwarf.

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______(3) (Total 11 marks)

Page 7 of 15 Q6. The absolute magnitude and spectral class of four stars W, X, Y and Z are plotted using the axes below.

(a) Draw and label, on the diagram above, the regions occupied by the main sequence, white dwarf stars and red giant stars. (2)

(b) The following observations were made for the star Alnilam in the constellation of Orion.

apparent magnitude: 1.7 distance from Earth: 1350 light years spectrum: strong hydrogen Balmer absorption lines

(i) Explain what is meant by apparent magnitude.

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(ii) Calculate the distance in parsecs of Alnilam from the Earth.

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(iii) Hence calculate the absolute magnitude of Alnilam.

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(iv) Which of the stars, W, X, Y or Z is Alnilam? Explain your answer.

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Page 8 of 15 ______(7)

(c) The stars shown on the graph could represent the position of a star at different times during its evolution. Write down the correct sequence, using some or all of the letters, that would best represent the evolution of the Sun starting from its present position.

______(1) (Total 10 marks)

Q7. (a) The graph shows the axes of a Hertzsprung–Russell (H–R) diagram.

(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:

Page 9 of 15 • 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.

absolute magnitude = ______(3)

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

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______(3) (Total 15 marks)

Q8. (a) Define the absolute magnitude of a star.

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

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(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)

Q9. The graph shows the variation of intensity with wavelength for the star 40 Eridani B.

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(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? Tick (✓) the correct answer.

Page 12 of 15 main

sequence

dwarf star

giant star

(1)

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

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______(2) (Total 8 marks)

Q10. (a) Define the term absolute magnitude.

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

Mark suitable scales on the absolute magnitude and temperature axes.

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temperature / K (2)

(c) Label a possible position of each of the following stars on the diagram above:

(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.

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Page 14 of 15 ______(3) (Total 10 marks)

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