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Date May 2017 Marks available 1 Reference code 17M.3.SL.TZ2.11
Level Standard level Paper Paper 3 Time zone Time zone 2
Command term Draw Question number 11 Adapted from N/A

Question

The diagram shows the structure of a typical main sequence star.

Star X is likely to evolve into a neutron star.

State the most abundant element in the core and the most abundant element in the outer layer.

[2]
a.

The Hertzsprung–Russell (HR) diagram shows two main sequence stars X and Y and includes lines of constant radius. R is the radius of the Sun.

M17/4/PHYSI/SP3/ENG/TZ2/11b

Using the mass–luminosity relation and information from the graph, determine the ratio \(\frac{{{\text{density of star X}}}}{{{\text{density of star Y}}}}\).

[3]
b.

On the HR diagram in (b), draw a line to indicate the evolutionary path of star X.

[1]
c.i.

Outline why the neutron star that is left after the supernova stage does not collapse under the action of gravitation.

[1]
c.ii.

The radius of a typical neutron star is 20 km and its surface temperature is 106 K. Determine the luminosity of this neutron star.

[2]
c.iii.

Determine the region of the electromagnetic spectrum in which the neutron star in (c)(iii) emits most of its energy.

[2]
c.iv.

Markscheme

core: helium

outer layer: hydrogen

 

Accept no other elements.

[2 marks]

a.

ratio of masses is \({\left( {\frac{{{{10}^4}}}{{{{10}^{ - 3}}}}} \right)^{\frac{1}{{3.5}}}} = {10^2}\)

ratio of volumes is \({\left( {\frac{{10}}{{{{10}^{ - 1}}}}} \right)^3} = {10^6}\)

so ratio of densities is \(\frac{{{{10}^2}}}{{{{10}^6}}} = {10^{ - 4}}\)

 

Allow ECF for MP3 from earlier MPs

[3 marks]

b.

line to the right of X, possibly undulating, very roughly horizontal

 

Ignore any paths beyond this as the star disappears from diagram.

[1 mark]

c.i.

gravitation is balanced by a pressure/force due to neutrons/neutron degeneracy/pauli exclusion principle

 

Do not accept electron degeneracy.

[1 mark]

c.ii.

L = \(\sigma \)AT 4 = 5.67 x 10–8 x 4\(\pi \) x (2.0 x 104)2 x (106)4

L = 3 x 1026 «W»
OR
L = 2.85 x 1026 «W»

 

Allow ECF for [1 max] if \(\pi \)r 2 used (gives 7 x 1026 «W »)

Allow ECF for a POT error in MP1.

[2 marks]

c.iii.

\(\lambda  = \frac{{2.9 \times {{10}^{ - 3}}}}{{{{10}^6}}} = 2.9 \times {10^{ - 9}}\) «m»

this is an X-ray wavelength

[2 marks]

c.iv.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.i.
[N/A]
c.ii.
[N/A]
c.iii.
[N/A]
c.iv.

Syllabus sections

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