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Date May 2013 Marks available 2 Reference code 13M.3.HL.TZ2.3
Level Higher level Paper Paper 3 Time zone Time zone 2
Command term State Question number 3 Adapted from N/A

Question

This question is about stellar evolution.

The Hertzsprung–Russell (HR) diagram shows the Sun, a star A and the main sequence.

Using the mass–luminosity relation LM3.5, determine the ratio of the mass of star A to the mass of the Sun.

[2]
a.

Star A will leave the main sequence and will evolve to become a neutron star. State the

(i) change in star A that marks its departure from the main sequence.

(ii) range of mass of a neutron star.

 

[2]
b.

Markscheme

\(\frac{{{L_{\rm{A}}}}}{{{L_{\rm{S}}}}} = 100 = {\left[ {\frac{{{M_{\rm{A}}}}}{{{M_{\rm{S}}}}}} \right]^{3.5}}\);
\(\left( {\frac{{{M_{\rm{A}}}}}{{{M_{\rm{S}}}}} = {{100}^{1/3.5}} = 3.7} \right) \approx 4\)
Award marks only if a ratio is calculated.

a.

(i) depletion of hydrogen in the core / fusion moves to outer layers;

(ii) 1.4MΘ<M<3MΘ
Allow between 2MΘ and 3MΘ as the upper bound OV limit.

b.

Examiners report

(stellar mass ratio) was well answered, although sometimes the working was poorly presented. Hydrogen depletion was usually not specifically mentioned.

a.

(b)(i) as the cause for a star to leave the main sequence. Many gave unnecessary information about the subsequent path to a neutron star. For (b)(ii) the upper or lower limits for the mass of a neutron star were known, but rarely both. The range 1.4Ms to 2.5Ms or 3Ms was allowed. Often the names of the limits were given, but not the values.

b.

Syllabus sections

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