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Date November 2017 Marks available 2 Reference code 17N.3.SL.TZ0.12
Level Standard level Paper Paper 3 Time zone Time zone 0
Command term Show Question number 12 Adapted from N/A

Question

Sirius is a binary star. It is composed of two stars, Sirius A and Sirius B. Sirius A is a main sequence star.

The Sun’s surface temperature is about 5800 K.

The image shows a Hertzsprung–Russell (HR) diagram.

The mass of Sirius A is twice the mass of the Sun. Using the Hertzsprung–Russell (HR) diagram,

State what is meant by a binary star.

[1]
a.

The peak spectral line of Sirius B has a measured wavelength of 115 nm. Show that the surface temperature of Sirius B is about 25 000 K.

[1]
b.

The mass of Sirius B is about the same mass as the Sun. The luminosity of Sirius B is 2.5 % of the luminosity of the Sun. Show, with a calculation, that Sirius B is not a main sequence star.

[2]
c.

Determine the radius of Sirius B in terms of the radius of the Sun.

[2]
d.i.

Identify the star type of Sirius B.

[1]
d.ii.

draw the approximate positions of Sirius A, labelled A and Sirius B, labelled B.

[1]
e.i.

sketch the expected evolutionary path for Sirius A.

[1]
e.ii.

Markscheme

two stars orbiting a common centre «of mass»

Do not accept “stars which orbit each other”

a.

«\(\lambda \) x = 2.9 x 10–3»

T = \(\frac{{2.9 \times {{10}^{ - 3}}}}{{115 \times {{10}^{ - 9}}}}\) = 25217 «K»

b.

use of the mass-luminosity relationship or \({\left( {\frac{{{M_{{\text{Sirius}}}}}}{{{M_{{\text{Sun}}}}}}} \right)^{3.5}}\) = 1

if Sirius B is on the main sequence then \(\left( {\frac{{{L_{\,{\text{Sirius}}\,{\text{B}}}}}}{{L{\,_{{\text{Sun}}}}}}} \right)\) = 1 «which it is not»

Conclusion is given, justification must be stated

Allow reverse argument beginning with luminosity

c.

\(\left( {\frac{{{L_{\,{\text{Sirius}}\,{\text{B}}}}}}{{L{\,_{{\text{Sun}}}}}}} \right)\) = 0.025

r Sirius = «\(\sqrt {0.025 \times {{\left( {\frac{{5800}}{{25000}}} \right)}^4}} \) =» 0.0085 r Sun

d.i.

white dwarf

d.ii.

Sirius A on the main sequence above and to the left of the Sun AND Sirius B on white dwarf area as shown

Both positions must be labelled 

Allow the position anywhere within the limits shown.

e.i.

arrow goes up and right and then loops to white dwarf area

e.ii.

Examiners report

[N/A]
a.
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b.
[N/A]
c.
[N/A]
d.i.
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d.ii.
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e.i.
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e.ii.

Syllabus sections

Option B: Engineering physics » Option B: Engineering physics (Additional higher level option topics) » B.4 – Forced vibrations and resonance (HL only)
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