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Date	November 2018	Marks available	1	Reference code	18N.3.HL.TZ0.18
Level	Higher level	Paper	Paper 3	Time zone	0 - no time zone
Command term	Show that	Question number	18	Adapted from	N/A

Question

The surface temperature of the star Epsilon Indi is 4600 K.

Determine the peak wavelength of the radiation emitted by Epsilon Indi.

[1]

a.i.

Using the axis, draw the variation with wavelength of the intensity of the radiation emitted by Epsilon Indi.

[2]

a.ii.

The following data are available for the Sun.

Surface temperature = 5800 K

Luminosity = ${L_ \odot }$

Mass = ${M_ \odot }$

Radius = ${R_ \odot }$

Epsilon Indi has a radius of 0.73 ${R_ \odot }$ . Show that the luminosity of Epsilon Indi is 0.2 ${L_ \odot }$ .

[2]

a.iii.

Epsilon Indi is a main sequence star. Show that the mass of Epsilon Indi is 0.64 ${M_ \odot }$ .

[1]

The Sun will spend about nine billion years on the main sequence. Calculate how long Epsilon Indi will spend on the main sequence.

[2]

Describe the stages in the evolution of Epsilon Indi from the point when it leaves the main sequence until its final stable state.

[3]

Markscheme

λ = « $\frac{{2.9 \times {{10}^{ - 3}}}}{{4600}}$ =» 630 «nm» ✔

a.i.

black body curve shape ✔

peaked at a value from range 600 to 660 nm ✔

a.ii.

$\frac{L}{{{L_ \odot }}} = {\left( {\frac{{0.73{R_ \odot }}}{{{R_ \odot }}}} \right)^2} \times {\left( {\frac{{4600}}{{5800}}} \right)^4}$ ✔

L = 0.211 ${L_ \odot }$ ✔

a.iii.

M = « ${0.21^{\frac{1}{{3.5}}}}\,{M_ \odot }$ =» 0.640 ${M_ \odot }$ ✔

$\frac{{{T_E}}}{{{T_ \odot }}} =$ « $\frac{{\frac{{{M_E}}}{{{L_E}}}}}{{\frac{{{M_ \odot }}}{{{L_ \odot }}}}} = \frac{{0.64}}{{0.21}} =$ » 3.0 ✔

T ≈ 27 billion years ✔

red giant ✔

planetary nebula ✔

white dwarf ✔

do NOT accept supernova, red supergiant, neutron star or black hole as stages

Examiners report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]

a.iii.

[N/A]

Syllabus sections

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

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Option D: Astrophysics » Option D: Astrophysics (Core topics)

Option D: Astrophysics

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