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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. 

[2]
a.

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 \(\frac{{{\rm{luminosity of star X}}}}{{{\rm{luminosity of the Sun}}}}\).

 

[3]
b.

On the Hertzsprung–Russell diagram, label the position of star X with the letter X.

 

[1]
c.

Markscheme

\(T = \frac{{2.9 \times {{10}^{ - 3}}}}{{3.0 \times {{10}^{ - 7}}}}\);
9700 (K);

a.

\(\frac{{{L_X}}}{{{L_S}}} = \frac{{\sigma {r_x}^2{T_x}^4}}{{\sigma {r_S}^2{T_S}^4}}\);
=\(\frac{{{{4.5}^2} \times {{9700}^4}}}{{{{5700}^4}}}\);
=170;

Accept answers that use T = 10000(K) to give an answer of 190.

 

 

 

b.

 

X marked correctly within range shown;

c.

Examiners report

 Was very well done in general.

a.

 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.

b.

Was well done in general.

c.

Syllabus sections

Option D: Astrophysics » Option D: Astrophysics (Core topics) » D.2 – Stellar characteristics and stellar evolution
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