| Date | November 2012 | Marks available | 2 | Reference code | 12N.3.SL.TZ0.14 |
| Level | Standard level | Paper | Paper 3 | Time zone | Time zone 0 |
| Command term | Draw and Show that | Question number | 14 | Adapted from | N/A |
Question
This question is about stars.
The Hertzsprung–Russell (HR) diagram shows the Sun, a star labelled A and the main sequence.
Star A is part of a binary star system. The diagram shows the orbit of star A and the orbit of its companion, star B.
The temperature of star A is TA, the temperature of star B is TB and \(\frac{{{T_A}}}{{{T_B}}} = 0.60\). The radius of star A is RA, the radius of star B is RB and \(\frac{{{R_A}}}{{{R_B}}} = 270\).
Show that the luminosity of star A is 9.4×103 times greater than the luminosity of star B.
The diagram below shows the spectrum of the stars as observed from Earth. The spectrum shows one line from star A and one line from star B, when the stars are in the position shown in the diagram (b).
On the spectrum draw lines to show the approximate positions of these spectral lines after the stars have completed one quarter of a revolution.
Markscheme
\(\frac{{{L_{\rm{A}}}}}{{{L_{\rm{B}}}}} = \frac{{\sigma 4\pi R_{\rm{A}}^2T_{\rm{A}}^4}}{{\sigma 4\pi R_{\rm{B}}^2T_{\rm{B}}^4}}\);
\(\frac{{{L_{\rm{A}}}}}{{{L_{\rm{B}}}}} = {0.60^4} \times {270^2}\) or look for 3 or more sig fig eg 9.45×103;
\(\left( {\frac{{{L_{\rm{A}}}}}{{{L_{\rm{B}}}}} = 9.4 \times {{10}^3}} \right)\)
Award [1] for each correct line.
The shifted lines are light grey in the diagram above. Ignore magnitude of shift.
Award [0] if more than two lines are drawn unless it is clear which lines are to be marked.
