| Date | May 2014 | Marks available | 2 | Reference code | 14M.3.HL.TZ1.3 |
| Level | Higher level | Paper | Paper 3 | Time zone | Time zone 1 |
| Command term | Determine | Question number | 3 | Adapted from | N/A |
Question
This question is about stellar distances.
The star Sirius A is 3 pc from Earth. The apparent brightness of Sirius A is 1.2×10–7Wm–2. Determine the luminosity of Sirius A.
The luminosity of the Sun is 3.8×1026 W. Determine the mass of Sirius A relative to the mass of the Sun. (Assume that n=3.5 in the mass–luminosity relation.)
Markscheme
\(L\left( { = 4\pi b{d^2}} \right) = 4 \times {\rm{\pi }} \times 1.2 \times {10^{ - 7}} \times {\left[ {8.1 \times {{10}^{16}}} \right]^{^2}}\);
9.9×1027(W);
Allow 1.3×1028(W) if candidates use 3 (pc) from (a).
\(\frac{{{{\rm{M}}_{{\rm{Sirius}}}}}}{{{{\rm{M}}_{{\rm{Sun}}}}}}\left( { = {{\left[ {\frac{{{{\rm{L}}_{{\rm{Sirius}}}}}}{{{{\rm{L}}_{{\rm{Sun}}}}}}} \right]}^{\frac{1}{{3.5}}}}} \right) = {\left[ {\frac{{9.9 \times {{10}^{27}}}}{{3.8 \times {{10}^{26}}}}} \right]^{\frac{1}{{3.5}}}}\);
\({{\rm{M}}_{{\rm{Sirius}}}} = 2.5{{\rm{M}}_{{\rm{Sun}}}}\);
Allow ECF from (b).
Examiners report
Some candidates had difficulty in manipulating a logarithmic equation. (b) discriminated well. Many candidates used the equation from the data booklet value in non-SI unit and forgot to convert pc to meters. This was not a surprise to the examining team. Quite a high number forgot to square the distance.
In (c), many candidates did not present their working in logical manner, especially those who did not understand mass-luminosity relations and incorrectly used the formula from data booklet.
