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