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Date	May 2018	Marks available	1	Reference code	18M.3.SL.TZ1.11
Level	Standard level	Paper	Paper 3	Time zone	1
Command term	Write down	Question number	11	Adapted from	N/A

Question

The graph shows the observed spectrum from star X.

M18/4/PHYSI/SP3/ENG/TZ1/11_01

The second graph shows the hydrogen emission spectrum in the visible range.

M18/4/PHYSI/SP3/ENG/TZ1/11_02

The following diagram shows the main sequence.

M18/4/PHYSI/SP3/ENG/TZ1/11.b

Suggest, using the graphs, why star X is most likely to be a main sequence star.

[2]

a.i.

Show that the temperature of star X is approximately 10 000 K.

[2]

a.ii.

Write down the luminosity of star X (L_X) in terms of the luminosity of the Sun (L_s).

[1]

b.i.

Determine the radius of star X (R_X) in terms of the radius of the Sun (R_s).

[3]

b.ii.

Estimate the mass of star X (M_X) in terms of the mass of the Sun (M_s).

[2]

b.iii.

Star X is likely to evolve into a stable white dwarf star.

Outline why the radius of a white dwarf star reaches a stable value.

[2]

Markscheme

the wavelengths of the dips correspond to the wavelength in the emission spectrum

the absorption lines in the spectrum of star X suggest it contains predominantly hydrogen

main sequence stars are rich in hydrogen

[2 marks]

a.i.

peak wavelength: 290 ± 10 «nm»

T = $\frac{{2.9 \times {{10}^{-3}}}}{{290 \times {{10}^{ - 9}}}}$ = «10 000 ± 400 K»

Substitution in equation must be seen.

Allow ECF from MP1.

[2 marks][

a.ii.

35 ± 5L_s

[1 mark]

b.i.

$\frac{{{L_{\text{X}}}}}{{{L_{\text{s}}}}} = \frac{{R_{\text{X}}^2 \times {\text{T}}_{\text{X}}^4}}{{R_{\text{s}}^2 \times {\text{T}}_{\text{s}}^4}}$

${R_{\text{X}}} = \sqrt {\frac{{{L_{\text{X}}}{\text{T}}_{\text{s}}^4}}{{{L_s}{\text{T}}_{\text{X}}^4}}} \times {R_{\text{s}}}$

${R_{\text{X}}} = \sqrt {\frac{{35 \times {{6000}^4}}}{{10\,{{000}^4}}}} \times {R_{\text{s}}}$ (mark for correct substitution)

R_X = 2.1R_s

Allow ECF from (b)(i).

Accept values in the range: 2.0 to 2.3R_s.

Allow TS in the range: 5500 K to 6500 K.

[3 marks]

b.ii.

M_X = ${(35)^{\frac{1}{{3.5}}}}$ M_s

M_X = 2.8M_s

Allow ECF from (b)(i).

Do not accept M_X = (35) $^{\frac{1}{{3.5}}}$ for first marking point.

Accept values in the range: 2.6 to 2.9M_s.

[2 marks]

b.iii.

the star «core» collapses until the «inward and outward» forces / pressures are balanced

the outward force / pressure is due to electron degeneracy pressure «not radiation pressure»

[2 marks]

Examiners report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]

b.i.

[N/A]

b.ii.

[N/A]

b.iii.

[N/A]

Syllabus sections

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

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17N.3.SL.TZ0.12a: State what is meant by a binary star.
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16N.3.SL.TZ0.15c:
Show, without calculation, that the radius of Alpha Centauri B is smaller than the radius of Alpha Centauri A.
17M.3.SL.TZ2.12c.ii:
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18N.3.SL.TZ0.12a.i:
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17N.3.SL.TZ0.12b:
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18N.3.HL.TZ0.18b:
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16N.3.SL.TZ0.15e:
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18M.3.SL.TZ1.11c:
Star X is likely to evolve into a stable white dwarf star.

Outline why the radius of a white dwarf star reaches a stable value.
19N.3.SL.TZ0.10c(iii):
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18M.3.SL.TZ1.11a.i:
Suggest, using the graphs, why star X is most likely to be a main sequence star.
17M.3.SL.TZ2.11b:
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.

Using the mass–luminosity relation and information from the graph, determine the ratio $\frac{{{\text{density of star X}}}}{{{\text{density of star Y}}}}$ .
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17M.3.SL.TZ2.11c.i:
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18M.3.SL.TZ2.11d.iii:
plot the position, using the letter G, of Gacrux.
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Option D: Astrophysics » Option D: Astrophysics (Core topics)

Option D: Astrophysics

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