| Date | November 2010 | Marks available | 2 | Reference code | 10N.3.HL.TZ0.E1 |
| Level | Higher level | Paper | Paper 3 | Time zone | Time zone 0 |
| Command term | Show that | Question number | E1 | Adapted from | N/A |
Question
This question is about the characteristics of the stars Procyon A and Procyon B.
The star Betelgeuse is about five times the mass of Regulus. One possible outcome of the final stage of the evolution of Betelgeuse is for it to become a black hole. State the
The luminosity of the main sequence star Regulus is \(150{\text{ }}{L_{\text{S}}}\). Assuming that, in the mass–luminosity relationship, \(n = 3.5\) show that the mass of Regulus is \(4.2{\text{ }}{M_{\text{S}}}\) where \({M_{\text{S}}}\) is the mass of the Sun.
(i) other possible outcome of the final stage of the evolution of Betelgeuse.
(ii) reason why the final stage in (j)(i) is stable.
Markscheme
\(\frac{{150}}{1} = {\left( {\frac{{{M_{\text{R}}}}}{1}} \right)^{3.5}}\)\(\,\,\,\,\,\)or\(\,\,\,\,\,\)\(150 = M_{\text{R}}^{3.5}\);
evidence of algebraic manipulation e.g. \({M_{\text{R}}} = {[150]^{\frac{1}{{3.5}}}}\);
\( = 4.2{\text{ }}{{\text{M}}_{\text{S}}}\)
To award [2] there must be evidence of algebraic manipulation shown.
(i) neutron star;
(ii) (because of) neutron degeneracy pressure / Pauli exclusion principle excludes further collapse;
Examiners report
Some candidates struggle with the manipulation of logs.
A significantly large number of candidates in (j) recognised that Betelgeuse might become a neutron star and that neutron degeneracy pressure would account for its final stability.
