IB Physics HL E 5 Fusion and Stars Questions

Practise IB Physics HL E.5 by analysing stellar fusion chains, binding energy, spectra and quantitative star-property evidence.

Exam points

Calculate binding-energy changes across fusion pathways and connect them to stellar energy production.
Use luminosity, spectra, Wien and Stefan–Boltzmann relationships to infer stellar properties.
Evaluate fusion-cycle evidence, stellar evolution indicators and uncertainty in extended HL data.

Covered syllabus points

E.5.1—Stellar equilibrium E.5.2—Fusion in stars E.5.3—Fusion conditions E.5.4—Stellar mass and evolution E.5.5—HR diagram regions E.5.6—Stellar parallax E.5.7—Stellar radii

[Maximum number: 6]

The diagram shows a simplified energy-balance model for the Earth surface-atmosphere system.

The following data are given:

\begin{aligned} \text { Average albedo of Earth } & =0.30 \\ \text { Average global temperature of the surface } & =288 \mathrm{~K} \\ \text { Average Earth-Sun distance } & =1.5 \times 10^{11} \mathrm{~m} \end{aligned}

(a)

The primary energy source of the Sun is the proton-proton (p-p) chain of fusion reactions. Four protons and two electrons produce a helium nucleus together with neutrinos and gamma photons. The overall reaction is:

4{ }_{1}^{1} \mathrm{p}+2{ }_{-1}^{0} \mathrm{e} \rightarrow{ }_{2}^{4} \mathrm{He}+2{ }_{0}^{0} v_{e}+4 \gamma

[ 2 ]

(i)

Outline the role of fusion reactions in maintaining a stable radius of the Sun.

[ 2 ]

(b)

The positions of the Sun and the star Antares are shown in the Hertzsprung-Russell (HR) diagram.

[ 4 ]

(i)

State the star type of Antares.

[ 1 ]

(ii)

Discuss how nuclear fusion processes in Antares are different from those in the Sun.

[ 3 ]

[Maximum number: 3]

Three stars A, B and C are labelled on the Hertzsprung-Russell (HR) diagram. $L_{\odot}$ is the Luminosity of the sun.

(a)

State the main element that is undergoing nuclear fusion in star C .

[ 1 ]

(b)

White dwarfs with similar volumes to each other are shown on the HR diagram.

Construct a line, on the HR diagram, to show the possible positions of other white dwarf stars with similar volumes to those marked on the HR diagram.

[ 2 ]

[Maximum number: 4]

Star A is a main sequence star.

The data for Star A and the Sun are given in a table.

(a)

State how physical stability is maintained in main sequence stars.

[ 1 ]

(b)

Explain why nuclear fusion in the core of the star occurs when the temperature and density exceed threshold values.

[ 2 ]

(c)

Calculate, in m , the distance to Star A from Earth.

[ 1 ]

$d=\left(\frac{1}{0.74}\right)(3.26)\left(9.46 \times 10^{15}\right)=4.2 \times 10^{16} \mathrm{~m}$

Distance must be stated in
metres.

[Maximum number: 2]

The diagram shows a simplified energy-balance model for the Earth surface-atmosphere system.

The following data are given:

\begin{aligned} \text { Average albedo of Earth } & =0.30 \\ \text { Average global temperature of the surface } & =288 \mathrm{~K} \\ \text { Average Earth-Sun distance } & =1.5 \times 10^{11} \mathrm{~m} \end{aligned}

4{ }_{1}^{1} \mathrm{p}+2{ }_{-1}^{0} \mathrm{e} \rightarrow{ }_{2}^{4} \mathrm{He}+2{ }_{0}^{0} v_{e}+4 \gamma

Outline the role of fusion reactions in maintaining a stable radius of the Sun.

[Maximum number: 1]

Three stars A, B and C are labelled on the Hertzsprung-Russell (HR) diagram. $L_{\odot}$ is the Luminosity of the sun.

State the main element that is undergoing nuclear fusion in star C .

[Maximum number: 2]

Star A is a main sequence star.

The data for Star A and the Sun are given in a table.

Explain why nuclear fusion in the core of the star occurs when the temperature and density exceed threshold values.

[Maximum number: 3]

Alpha Centauri A and B form the closest binary star system to the Earth. This binary star system is the third brightest stellar object in the night sky.

(a)

Proxima Centauri is a main sequence star with a mass of $0.12 M_{\odot}$ .

Compare the times for which Proxima Centauri and Alpha Centauri A are main sequence stars.

[ 2 ]

«L=E/t and E proportional to M so» t inversely proportional to $M^{2.5}$
OR
$\frac{t_P}{t_{\alpha}}=\left(\frac{1.12}{0.12}\right)^{2.5}$
OR faster fusion rate to hydrogen available in Alpha Centauri A

Proxima Centauri stays longer on main sequence OR
$t_P=270t_{\alpha}$

Award [1] for a correct but incomplete reason, e.g. larger luminosity, or smaller mass, with the correct conclusion.

(b)

Explain the relationship between binary star systems and type I a supernovae.

[ 1 ]

[Maximum number: 1]

The diagram shows a simplified energy-balance model for the Earth surface-atmosphere system.

The following data are given:

\begin{aligned} \text { Average albedo of Earth } & =0.30 \\ \text { Average global temperature of the surface } & =288 \mathrm{~K} \\ \text { Average Earth-Sun distance } & =1.5 \times 10^{11} \mathrm{~m} \end{aligned}

The positions of the Sun and the star Antares are shown in the Hertzsprung-Russell (HR) diagram.

State the star type of Antares.

[Maximum number: 1]

Star A is a main sequence star.

The data for Star A and the Sun are given in a table.

Calculate, in m , the distance to Star A from Earth.

$d=\left(\frac{1}{0.74}\right)(3.26)\left(9.46 \times 10^{15}\right)=4.2 \times 10^{16} \mathrm{~m}$

Distance must be stated in
metres.

[Maximum number: 4]

Alpha Centauri A and B is a binary star system in the main sequence.

(a)

The luminosity of the Sun is $3.8 \times 10^{26} \mathrm{~W}$ . Calculate the radius of Alpha Centauri A.

[ 2 ]

$r=\sqrt{\frac{1.5\times3.8\times10^{26}}{5.67\times10^{-8}\times4\pi\times5800^{4}}}=8.4\times10^{8}\ \mathrm m$

(b)

Show, without calculation, that the radius of Alpha Centauri B is smaller than the radius of Alpha Centauri A.

[ 2 ]

$A=\frac{L}{\sigma T^{4}}$ ;
B and A have similar temperatures.

Therefore, their areas are in the ratio of their luminosities, so the radius of B is less than that of A.

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Covered syllabus points

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