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Date May 2018 Marks available 2 Reference code 18M.3.SL.TZ1.11
Level Standard level Paper Paper 3 Time zone Time zone 1
Command term Estimate 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 (LX) in terms of the luminosity of the Sun (Ls).

[1]
b.i.

Determine the radius of star X (RX) in terms of the radius of the Sun (Rs).

[3]
b.ii.

Estimate the mass of star X (MX) in terms of the mass of the Sun (Ms).

[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]
c.

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

OR

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 ± 5Ls

[1 mark]

b.i.

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

OR

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

 

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

RX = 2.1Rs

 

Allow ECF from (b)(i).

Accept values in the range: 2.0 to 2.3Rs.

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

[3 marks]

b.ii.

MX = \({(35)^{\frac{1}{{3.5}}}}\)Ms

MX = 2.8Ms

 

Allow ECF from (b)(i).

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

Accept values in the range: 2.6 to 2.9Ms.

[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]

c.

Examiners report

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

Syllabus sections

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