| Date | May 2013 | Marks available | 2 | Reference code | 13M.3.SL.TZ1.14 |
| Level | Standard level | Paper | Paper 3 | Time zone | Time zone 1 |
| Command term | Show that | Question number | 14 | Adapted from | N/A |
Question
This question is about the properties of a star.
The peak in the radiation spectrum of a star X is at a wavelength of 300 nm.
Show that the surface temperature of star X is about 10000 K.
The radius of star X is 4.5 RS where RS is the radius of the Sun. The surface temperature of the Sun is 5.7×103 K.
Determine the ratio \(\frac{{{\rm{luminosity of star X}}}}{{{\rm{luminosity of the Sun}}}}\).
On the Hertzsprung–Russell diagram, label the position of star X with the letter X.
Markscheme
\(T = \frac{{2.9 \times {{10}^{ - 3}}}}{{3.0 \times {{10}^{ - 7}}}}\);
9700 (K);
\(\frac{{{L_X}}}{{{L_S}}} = \frac{{\sigma {r_x}^2{T_x}^4}}{{\sigma {r_S}^2{T_S}^4}}\);
=\(\frac{{{{4.5}^2} \times {{9700}^4}}}{{{{5700}^4}}}\);
=170;
Accept answers that use T = 10000(K) to give an answer of 190.
X marked correctly within range shown;
Examiners report
Was very well done in general.
Many answered (b) well, but a large minority made mistakes with powers or tried to evaluate both luminosities then find the ratio and failed in the process. A lot of poor algebra and messy working was evident.
Was well done in general.
