IB Physics HL E.5 Fusion and stars Questions

SLSL HLHL

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

110 questions in this syllabus scope, with question parts counted together.

Exam points & syllabus

Exam points

Explain a stable stellar radius through balanced outward radiation or thermal pressure and inward gravitational pressure, giving both directions.
When required, link the outward effect to energy or photons produced by core fusion; explain the photon and gravitational interactions.
Keep force-to-force or pressure-to-pressure comparisons consistent; an unexplained “hydrostatic equilibrium” may earn only partial credit.
For the more massive star, link greater inward gravitational pressure to greater balancing outward pressure and faster hydrogen use.
Identify nuclear fusion as the stellar energy source and hydrogen-to-helium fusion as the main-sequence process.
For the stated star–planet comparison, use ongoing core fusion in the main-sequence star as a complete distinguishing feature.
For a constant-luminosity lifetime, divide Lt by energy per supplied fusion cycle, then multiply by four proton masses for the hydrogen consumed.
Explain massive-star fusion layers by different reactions at different depths, with heavier elements toward the core and lighter elements outside.
Distinguish main-sequence H-to-He fusion from later He-to-carbon fusion once core helium ignites; do not assume ignition from a red-giant label alone.
For Antares versus the Sun, cover what fuses, fusion rate or core conditions, and the separate regions or shells where fusion occurs.
Explain high fusion temperature through high nuclear KE overcoming Coulomb repulsion, or high KE bringing nuclei into strong-force range.
State both high temperature and high density for stellar fusion, linking sufficient energy to close approach and strong nuclear attraction.
A collapsed nebula becomes a star when its core is hot enough for hydrogen fusion; higher temperature favours fusion while beta decay is unaffected.
For heavier-element fusion, link greater stellar mass to higher core pressure and the temperature or density needed against greater nuclear repulsion.
Compare matched evolutionary stages: Sun-like stars form red giants, planetary nebulae and white dwarfs; massive stars follow the supergiant route.
For the massive-star route, give red supergiant, supernova and neutron-star or black-hole remnant in order, including intermediate phases.
Use the remnant’s mass to explain a neutron-star versus black-hole outcome; do not substitute the original stellar mass for remnant mass.
For the stated 1.3-solar-mass star, include mass loss through planetary-nebula ejection before the remaining core becomes a white dwarf.
Describe initial red-giant expansion through core hydrogen exhaustion, hydrogen-shell fusion and an expanding, cooling surface.
Identify white-dwarf radiation as residual thermal or internal energy and predict decreasing luminosity as the remnant cools.
Explain main-sequence lifetime by fuel available relative to fusion rate; a more massive star can exhaust its fuel sooner despite having more hydrogen.
When L ∝ M³·⁵ and lifetime ∝ M/L are explicitly supplied, show the luminosity and lifetime ratios with algebra before numerical substitution.
For the supplied helium-fusing cores, explain faster fusion by higher core temperature; greater mass or pressure alone is insufficient.
Read HR coordinates using luminosity upward and temperature decreasing to the right; use both quantities to identify the stellar region.
Distinguish hot faint white dwarfs from cool luminous giants; for Barnard’s star give separate low-temperature and low-luminosity rejection reasons.
Plot stars from their actual supplied or derivable data and labels; place the Sun near 5800 K and one solar luminosity.
For Sirius, label A on the main sequence above and left of the Sun and B in the hot faint white-dwarf region; both labels are required.
Draw the main sequence down and right on the supplied diagram; for the massive star draw its departure toward red supergiants.
For a Sun-like HR evolutionary path, include and label the red-giant and white-dwarf regions, following the actual temperature-axis direction.
For similar white-dwarf volumes, draw or extend the same constant-radius trend through the three identified white-dwarf points.
To reject β Ori as main sequence, compare its much greater luminosity AND similar temperature with Vega before stating the conclusion.
Use the rubric’s specific class where required: Antares is a red supergiant, and the supplied evolutionary order is Y, Z, X.
Measure stellar parallax relative to distant background stars at positions six months apart, stating the reference stars explicitly.
Use 1 AU with the half-shift p or 2 AU with the full six-month shift; label the orbital baseline, stellar distance and angle consistently.
Apply d(pc) = 1/p(arcsec); halve a total extreme-position shift before taking the reciprocal, but do not halve an angle already defined as p.
Convert pc to ly, metres or AU as requested; use 1 pc ≈ 3.26 ly and the supplied light-year and AU lengths consistently.
For the Alpha Centauri show-that distance, show the full substitution or an extra significant figure beyond the rounded target.
Explain the distance limitation through a parallax angle too small to measure reliably; avoid treating a historical distance threshold as universal.
For equal luminosities, combine b ∝ 1/d² and p ∝ 1/d: the brighter star has larger parallax, with the square-root brightness factor.
For an absolute stellar radius, rearrange L = 4πR²σT⁴ to R = √[L/(4πσT⁴)] and retain the requested length unit.
For radius ratios, use R₁/R₂ = √(L₁/L₂)(T₂/T₁)²; at equal temperature only the square root of luminosity ratio remains.
For binary stars at equal distance, substitute the apparent-brightness ratio for luminosity ratio and check the requested radius-ratio direction.
Use actual luminosity and temperature changes in evolutionary-stage radius ratios; the supplied white-dwarf/red-giant radius ratio is 9 × 10⁻⁶.
For a supplied qualitative comparison at similar temperatures, use the luminosity difference to argue the radius order without claiming exact equal T.
For the inverse Stefan–Boltzmann task, show L₁/L₂ = (R₁/R₂)²(T₁/T₂)⁴; the given Gomeisa data give about 210, not just the quoted 200.
When luminosity and radius are supplied, take the fourth root to find the temperature ratio; 280/(3.2)² gives TX/TSun ≈ 2.3.
For the commercial fusion comparison, give two distinct difficulties, such as producing the required high temperature and containing the hot fuel.
State a specific accepted fusion advantage in the given comparison, such as greater energy per unit fuel mass, rather than merely “more energy”.
For element formation, distinguish stellar fusion up to the iron region from neutron-capture production of heavier nuclei.

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

Exam points

State that outward radiation or thermal pressure balances inward gravitational pressure; name gravitational pressure or force explicitly.
Link the outward pressure to energy or photons produced by fusion in the core when explaining why the Sun or stated star does not collapse.
Explain pressure origins: photons exert outward forces on stellar particles, while gravitational attraction between particles or layers acts inward.
Use force-to-force or pressure-to-pressure language consistently; merely naming hydrostatic equilibrium without explanation may earn only partial credit.
For the more massive main-sequence star, link greater gravitational pressure to greater required outward pressure and faster hydrogen fusion.

[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}

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

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

Exam points

Identify nuclear fusion as the process supplying stellar energy; do not replace it with an unexplained statement that the star is burning.
Define a main-sequence star by hydrogen fusion into helium, and use the actual HR-diagram position before identifying its fuel.
For the stated star–planet comparison, use ongoing core fusion in the main-sequence star as a complete distinguishing feature.
For a constant-luminosity lifetime estimate, calculate fusion events from Lt/Q, then multiply by the mass of four protons per supplied p–p cycle.
Explain the supplied massive-star layers through successive fusion reactions: heavier elements occur deeper inside and lighter elements farther out.
Compare the Sun-mass stages: H fuses to He on the main sequence; later, once core helium ignites, He fusion produces carbon.
For Antares versus the Sun, cover all three rubric dimensions: elements fused, fusion rate or core conditions, and separate fusion shells or regions.

[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 .

Exam points

Link high temperature to high nuclear KE, then to overcoming Coulomb repulsion; state both links rather than only saying fusion needs heat.
Alternatively, explain that high KE brings nuclei within the short range of the strong force, and high temperature provides that KE.
For stellar fusion choose both high temperature and high density; explain the need for sufficient energy and nuclei close enough for strong attraction.
A collapsed nebula forms a star when its core becomes hot enough for hydrogen fusion to begin.
In the stated comparison, higher temperature favours fusion through greater nuclear KE and collision probability, while beta decay is unaffected.
For heavier-element fusion, link greater stellar mass to higher core pressure and temperature or density needed against greater nuclear repulsion.

[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.

Exam points

Compare matched stages: a Sun-like star becomes a red giant, ejects a planetary nebula and leaves a white dwarf; a massive star has a different route.
For the massive-star route, name red supergiant, supernova and a neutron-star or black-hole remnant in the required order.
When comparing final fates, include the intermediate envelope-ejection or supernova stage as well as both final remnants.
Explain that the mass of the remnant determines whether the massive star ends as a neutron star or black hole.
On the given massive-star HR diagram, draw the track roughly horizontally to the right from X; do not force the remnant to stay on the chart.
Plot Alpha Centauri A using its supplied luminosity and temperature, then draw a path up and right before returning toward the white-dwarf region.
For the supplied two-solar-mass Sirius A, show an HR path up and right toward the giant region, then a loop toward white dwarfs.
Discuss mass loss explicitly in the stated 1.3-solar-mass star: red giant, planetary-nebula ejection with a remaining core, then white dwarf.
For Aldebaran’s future, describe outer-envelope evolution, a planetary-nebula phase and the exposed remaining core using a complete accepted route.
Explain the Sun’s initial red-giant expansion through exhausted core hydrogen, continuing hydrogen-shell fusion and expansion with surface cooling.
Identify a white dwarf’s emitted energy as residual thermal or internal energy, rather than ongoing nuclear fusion.
Predict decreasing white-dwarf luminosity as it cools with time.
Explain shorter main-sequence life by faster fusion relative to the available fuel; greater fuel mass alone does not guarantee a longer life.
For the given Proxima–Alpha Centauri comparison, explain why Alpha Centauri A uses its available hydrogen faster and Proxima remains longer.
When both t ∝ M/L and L ∝ M³·⁵ are supplied, derive t ∝ M⁻²·⁵; the stated 2.2-solar-mass star lasts about 1/7 of the Sun’s time.
For the stated helium-fusing cores, link higher core temperature to a higher fusion rate; greater mass or pressure alone is insufficient.
Relate a massive star’s heavier-element fusion to greater core pressure and the higher temperature or density needed against nuclear repulsion.
For the given low-mass Vega stage, identify a white dwarf and describe its compact, hot or low-luminosity properties as the rubric requests.
Describe the supplied type II event by a red supergiant whose core collapses and explodes.

[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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