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Date May 2011 Marks available 2 Reference code 11M.3.HL.TZ1.4
Level Higher level Paper Paper 3 Time zone Time zone 1
Command term Show that Question number 4 Adapted from N/A

Question

This question is about the main sequence star Khad (Phi Orionis).

The luminosity of Khad is 2.0×104 LS, where LS is the luminosity of the Sun.

Assuming that the exponent n in the mass–luminosity relation is 3.5, show that the mass of Khad is about 17 solar masses.

[2]
a.

Outline the likely evolution of the star Khad after it leaves the main sequence.

[3]
b.

Markscheme

\(\frac{{{L_{\rm{K}}}}}{{{L_{\rm{S}}}}} = {\left[ {\frac{{{m_{\rm{K}}}}}{{{m_{\rm{S}}}}}} \right]^{3.5}}\);
\(m = {\left[ {\frac{{{L_{\rm{K}}}}}{{{L_{\rm{S}}}}} \times {m_{\rm{S}}}^{3.5}} \right]^{\frac{1}{{3.5}}}} = {\left[ {2.0 \times {{10}^4}} \right]^{\frac{1}{{3.5}}}}{m_{\rm{S}}}{\rm{ = 16.9}}{{\rm{m}}_{\rm{S}}}\);
hence mK≈17mS

a.

Khad will become a red supergiant/superred/superred giant;
a supernova will take place;
the core/remnant will form a neutron star or black hole;

b.

Examiners report

[N/A]
a.
[N/A]
b.

Syllabus sections

Option D: Astrophysics » Option D: Astrophysics (Core topics) » D.2 – Stellar characteristics and stellar evolution
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