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Date May 2017 Marks available 2 Reference code 17M.3.SL.TZ1.9
Level Standard level Paper Paper 3 Time zone Time zone 1
Command term Estimate Question number 9 Adapted from N/A

Question

Theta 1 Orionis is a main sequence star. The following data for Theta 1 Orionis are available.

Luminosity L = 4 × 105 L\(_ \odot \)
Radius R = 13R\(_ \odot \)
Apparent brightness b = 4 × 10–11 b\(_ \odot \) 

 

where L\(_ \odot \), R\(_ \odot \) and b\(_ \odot \) are the luminosity, radius and apparent brightness of the Sun.

State what is meant by a main sequence star.

[1]
a.i.

Show that the mass of Theta 1 Orionis is about 40 solar masses.

[1]
a.ii.

The surface temperature of the Sun is about 6000 K. Estimate the surface temperature of Theta 1 Orionis.

[2]
a.iii.

Determine the distance of Theta 1 Orionis in AU.

[2]
a.iv.

Discuss how Theta 1 Orionis does not collapse under its own weight.

[2]
b.

The Sun and Theta 1 Orionis will eventually leave the main sequence. Compare and contrast the different stages in the evolution of the two stars.

[3]
c.

Markscheme

stars fusing hydrogen «into helium»

[1 mark]

a.i.

\(M = {M_ \odot }{\left( {4 \times {{10}^5}} \right)^{\frac{1}{{3.5}}}} = 39.86{M_ \odot }\)

«\(M \approx 40{M_ \odot }\)»

 

Accept reverse working.

[1 mark]

a.ii.

\(4 \times {10^5} = {13^2} \times \frac{{{T^4}}}{{{{6000}^4}}}\)

\(T \approx 42\,000\) «K»

 

Accept use of substituted values into \(L = \sigma \)4\(\pi \)R2T4.

Award [2] for a bald correct answer.

[2 marks]

a.iii.

\(4 \times {10^{ - 11}} = 4 \times {10^5} \times \frac{{1{\text{A}}{{\text{U}}^2}}}{{{d^2}}}\)

\(d = 1 \times {10^8}\) «AU»

 

Accept use of correct values into \(b = \frac{L}{{4\pi {d^2}}}\).

[2 marks]

a.iv.

the gravitation «pressure» is balanced by radiation «pressure»

that is created by the production of energy due to fusion in the core / OWTTE

 

Award [1 max] if pressure and force is inappropriately mixed in the answer.

Award [1 max] for unexplained "hydrostatic equilibrium is reached".

[2 marks]

b.

the Sun will evolve to become a red giant whereas Theta 1 Orionis will become a red super giant

the Sun will explode as a planetary nebula whereas Theta 1 Orionis will explode as a supernova

the Sun will end up as a white dwarf whereas Theta 1 Orionis as a neutron star/black hole

[3 marks]

c.

Examiners report

[N/A]
a.i.
[N/A]
a.ii.
[N/A]
a.iii.
[N/A]
a.iv.
[N/A]
b.
[N/A]
c.

Syllabus sections

Option D: Astrophysics » Option D: Astrophysics (Core topics) » D.1 – Stellar quantities
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