DP Physics (last assessment 2024)

Question 19M.3.SL.TZ1.11

Date	May 2019	Marks available	[Maximum mark: 13]	Reference code	19M.3.SL.TZ1.11
Level	SL	Paper	3	Time zone	TZ1
Command term	Calculate, Determine, Label, Outline, Predict, Show that, State	Question number	11	Adapted from	N/A

11.

[Maximum mark: 13]

19M.3.SL.TZ1.11

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

The following data are available for the mass and radius of star X where M is the mass of the Sun and R is the radius of the Sun:

M_X = 5.0 M

R_X = 3.2 R

(a.i)

Show that the luminosity of star X is about 280 times greater than the luminosity of the Sun L.

[1]

Markscheme

${L_x} = {5.0^{3.5}}{L_ \odot } = 279.5{L_ \odot }$ ✔

Correct working or answer to 4 sig figs required.

Examiners report

Star evolution. This question is well designed, with varying degrees of difficulty and a sound capacity to discriminate levels.
(a) The luminosity of the star X was well compared to the luminosity of the Sun by almost all candidates, but the presentation of the work was often poor. The development of direct proportional ratios and the manipulation of equations were often misused.

(a.ii)

Determine the ratio $\frac{{{\text{surface temperature of star X}}}}{{{\text{surface temperature of the Sun}}}}$ .

[2]

Markscheme

$\frac{{{L_x}}}{{{L_ \odot }}} = 280 = \frac{{R_x^2}}{{R_ \odot ^2}}\frac{{T_x^4}}{{T_ \odot ^4}}$ ✔

$\frac{{{T_x}}}{{{T_ \odot }}} « = \sqrt[4]{{\frac{{280}}{{{{3.2}^2}}}}} » = 2.3$ ✔

Award [2] for bald correct answer.

Examiners report

Star evolution. This question is well designed, with varying degrees of difficulty and a sound capacity to discriminate levels.
In (ii), when conducting the ratio calculations, many omitted the powers in the formulas such as 3.22 and T4.

The parallax angle for star X is 0.125 arc-second.

(b.i)

Outline how the parallax angle of a star can be measured.

[2]

Markscheme

the position of the star is recorded 6 months apart
OR
the radius/diameter of the Earth orbit clearly labelled on a diagram ✔

the parallax is measured from the shift of the star relative to the background of the distant stars ✔

For MP2 accept a correctly labelled parallax angle on a diagram.

Award MP2 only if background distance stars are mentioned.

Examiners report

Measurement of parallax angle was well mastered by most of the candidates, however, some of them omitted to mention the importance of the background stars as a reference. Unit conversion in ii) was also well mastered by most of the candidates.

(b.ii)

Show that the distance to star X is 1.6 × 10⁶ AU.

[2]

Markscheme

d = $\frac{1}{0.125}$ = 8.0 «pc» ✔

d = 8.0 × 3.26 × $\frac{{9.46 \times {{10}^{15}}}}{{1.5 \times {{10}^{11}}}}$ «AU» ✔

«= 1.64 × 10⁶ AU»

Examiners report

Unit conversion in ii) was also well mastered by most of the candidates.

(b.iii)

The apparent brightness of the Sun is 1400 Wm^–2. Calculate, in Wm^–2, the apparent brightness of star X.

[2]

Markscheme

ALTERNATIVE 1

$\frac{{{b_x}}}{{1400}} = \frac{{\frac{{280}}{{4\pi {{\left( {1.6 \times {{10}^6}} \right)}^2}}}}}{{\frac{1}{{4\pi {{\left( 1 \right)}^2}}}}}$

${b_x} = \frac{{279.5}}{{4\pi \times {{\left( {1.6 \times {{10}^6} \times 1.5 \times {{10}^{11}}} \right)}^2}}}{\text{ and }}\frac{{{L_ \odot }}}{{4\pi \times {{\left( {1.5 \times {{10}^{11}}} \right)}^2}}}$ ✔

${b_x} = 1.5 \times {10^{ - 7}}$ «W m^–2» ✔

ALTERNATIVE 2

$\frac{{{b_x}}}{{{b_ \odot }}} = \frac{{{L_x}}}{{{L_ \odot }}} \times \left( {\frac{{d_ \odot ^2}}{{d_x^2}}} \right)$ OR $\frac{{{b_x}}}{{{b_ \odot }}} = \frac{{280}}{{{{\left( {1.6 \times {{10}^6}} \right)}^2}}}$ OR $\frac{{{b_x}}}{{{b_ \odot }}} = 1.094 \times {10^{ - 10}}W{m^{ - 2}}$ ✔

${b_x} = 1.09375 \times {10^{ - 10}} \times 1400$ ${b_x} = 1.5 \times {10^{ - 7}}W{m^{ - 2}}$ ✔

Award [2] for bald correct answer.

Allow ECF from MP1 to MP2

Examiners report

Part iii) proved to be very difficult for most of the average candidates with many experiencing difficulties working through the algebraic manipulations required. Many students mixed units or forgot to square the distances.

Star X will evolve to become a white dwarf star D.

(c.i)

Label, on the HR diagram, the region of white dwarf stars.

[1]

Markscheme

✔

Allow any region with L below Sun and left to the main sequence.

Examiners report

The region of white dwarfs stars was well labelled on the HR diagram.

(c.ii)

Outline the condition that prevents star D from collapsing further.

[1]

Markscheme

an electron degeneracy «pressure develops that opposes gravitation»/reference to Pauli principle ✔

Examiners report

Electron degeneracy pressure was well identified by most of the candidates.

(c.iii)

Star D emits energy into space in the form of electromagnetic radiation. State the origin of this energy.

[1]

Markscheme

thermal energy/internal energy ✔

Examiners report

The origin of the energy emitted to space from white dwarfs was only well stated by better candidates. Many mentioned different fusion reactions and thus did not recognize that the star had ceased this type of energy production.

(c.iv)

Predict the change in luminosity of star D as time increases.

[1]

Markscheme

«temperature decreases so» luminosity decreases ✔

Examiners report

The decrease in the luminosity of the dwarf star was well predicted by most of the candidates.

Question 19M.3.SL.TZ1.11

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