E.5 Fusion and stars
Practice exam-style IB Physics questions for Fusion and stars, aligned with the syllabus and grouped by topic.
Question 1
A main-sequence star has approximately constant radius for a long period of time. What maintains this stability?
A.
Outward gravitational pressure balances inward radiation pressure.
B.
Nuclear forces between all particles balance the weight of the star.
C.
Outward thermal and radiation pressure balance inward gravitational attraction.
D.
The star is supported by a rigid solid surface surrounding the plasma.
Question 2
In the overall proton–proton chain, what is the main product formed from four hydrogen nuclei?
A.
One carbon-12 nucleus, with electrons and energy released.
B.
One helium-4 nucleus, with positrons, neutrinos and energy released.
C.
Two helium-3 nuclei, with no change in rest mass.
D.
Four deuterium nuclei, with gamma radiation absorbed.
Question 3
Fusion in a stellar core requires both high temperature and high density. What is the role of high density?
A.
It decreases the binding energy of helium nuclei.
B.
It increases the frequency of collisions between nuclei.
C.
It changes photons into massive particles in the core.
D.
It removes the electric repulsion between protons.
Question 4
A star has a much greater initial mass than the Sun. Compared with the Sun, its main-sequence lifetime is expected to be
A.
longer because its stronger gravity prevents fusion.
B.
shorter because its fusion rate is much greater.
C.
longer because high luminosity reduces energy loss.
D.
shorter because it contains less hydrogen fuel.
Question 5
A star is modelled as a sphere of hot plasma.
State what is meant by hydrostatic equilibrium in a star.
[1]
Identify one outward pressure that can contribute to this equilibrium.
[1]
Question 6
A stellar spectrum contains absorption lines.
State what absorption lines can reveal about a star.
[1]
Distinguish between information obtained from absorption lines and from the black-body peak.
[1]
Question 7
On a Hertzsprung–Russell diagram, where are white dwarfs found?
A.
Upper right, where stars are cool but high in luminosity.
B.
Lower left, where stars are hot but low in luminosity.
C.
Upper left, where stars are hot and very luminous.
D.
Lower right, where stars are cool and very luminous.
Question 8
A star has a parallax angle of 0.20 arcsecond. What is its distance?
A.
0.20 pc
B.
20 pc
C.
2.0 pc
D.
5.0 pc
Question 9
The peak wavelength in the black-body spectrum of a star is shorter than that of the Sun. What can be concluded about the star?
A.
Its composition must be pure hydrogen.
B.
Its radius must be greater than the Sun’s.
C.
Its surface temperature is greater than the Sun’s.
D.
Its luminosity must be less than the Sun’s.
Question 10
In the first step of the proton–proton chain, a positron and an electron neutrino are emitted. What interaction is responsible for the conversion of a proton into a neutron?
A.
Gravitational interaction
B.
Strong interaction
C.
Electromagnetic interaction
D.
Weak interaction
Question 11
A stellar core remnant has mass greater than the Chandrasekhar limit but less than the Oppenheimer–Volkoff limit. The most likely compact remnant is a
A.
neutron star supported by neutron degeneracy pressure.
B.
main-sequence star supported by thermal pressure.
C.
red giant supported by radiation from shell fusion.
D.
white dwarf supported by electron degeneracy pressure.
Question 12
Why does fusion in a high-mass star not continue to release energy efficiently after the core reaches iron-group nuclei?
A.
The strong nuclear interaction disappears inside iron nuclei.
B.
Iron nuclei contain no protons to fuse with other nuclei.
C.
Iron-group nuclei have among the highest binding energies per nucleon.
D.
The core temperature becomes exactly zero at iron formation.
Question 13
Solar neutrinos provide direct evidence for fusion in the Sun because they
A.
are absorbed completely before reaching Earth.
B.
are produced in core fusion reactions and escape with little interaction.
C.
are photons with energies in the visible spectrum.
D.
are emitted only by the photosphere of a cool star.
Question 14
In the proton–proton chain, four hydrogen nuclei are converted into one helium nucleus.
State the equation used to calculate the energy released from a mass decrease.
[1]
Explain why energy is released in this fusion process.
[1]
Question 15
A protostar contracts under gravity before becoming a main-sequence star.
State one change in the core as the protostar contracts.
[1]
Explain why high temperature is needed for fusion.
[1]
Question 16
A star with a mass similar to the Sun leaves the main sequence.
State the immediate reason why the core contracts.
[1]
Outline two later stages in its evolution.
[1]
Question 17
A nearby star has a measured parallax angle of 0.125 arcsecond.
Calculate its distance in parsec.
[1]
State why parallax measurements are more difficult for more distant stars.
[1]
Question 18
The graph shows the apparent angular shift of a nearby star against background stars over one year.
Determine the parallax angle of the star from the graph.
[1]
Calculate the distance to the star in parsec.
[1]
Suggest one reason why repeated observations over more than one year improve the distance estimate.
[1]
Question 19
The graph shows how the rate of fusion events in a stellar core depends on core temperature for two different core densities.
Describe the effect of increasing temperature on fusion rate.
[1]
Compare the fusion rates at the two densities for the same temperature.
[1]
Explain why both variables affect the fusion rate.
[1]
Question 20
Star X has the same luminosity as the Sun but twice the Sun’s surface temperature. What is the radius of X in solar radii?
A.
0.25 R☉
B.
0.50 R☉
C.
4.0 R☉
D.
2.0 R☉
Question 21
Two stars have the same luminosity. Star X has a surface temperature four times that of star Y. What is RX/RY?
A.
4
B.
1/4
C.
16
D.
1/16
Question 22
A fusion reaction has a mass defect of 0.028 u. What energy is released? Use 1 u c² = 931.5 MeV.
A.
0.030 MeV
B.
3.3 × 10⁴ MeV
C.
9.3 × 10² MeV
D.
26 MeV
Question 23
A star is at a distance of 8.0 pc. What is its approximate distance in light years? Use 1 pc = 3.26 ly.
A.
26 ly
B.
8.0 ly
C.
3.09 × 10¹⁶ ly
D.
2.45 ly
Question 24
A star lies on a line of constant radius on an HR diagram. Moving along the line to higher surface temperature, what happens to luminosity?
A.
It increases in proportion to T⁴.
B.
It remains constant because radius is constant.
C.
It decreases in proportion to T⁻².
D.
It increases in proportion to T.
Question 25
The HR diagram is used to classify stars.
State the quantities normally plotted on the vertical and horizontal axes.
[1]
Describe the position and properties of red giants on an HR diagram.
[1]
Question 26
A star has luminosity 9.0 L☉ and surface temperature equal to the Sun’s surface temperature.
Write the comparison form of the Stefan–Boltzmann law for a star and the Sun.
[1]
Calculate the radius of the star in solar radii.
[1]
Question 27
The first step of the proton–proton chain is slow even at the temperature of the solar core.
State the particle emitted with a positron in this step.
[1]
Explain why this step limits the rate of hydrogen fusion in Sun-like stars.
[1]
Question 28
A high-mass star develops an onion-like shell structure late in its life.
State what is meant by an onion-like shell structure.
[1]
Explain why the core eventually cannot gain energy by fusing iron-group nuclei.
[1]
Question 29
Compact stellar remnants can be supported by degeneracy pressure.
State the approximate value of the Chandrasekhar limit.
[1]
Distinguish between electron degeneracy pressure and neutron degeneracy pressure in stellar remnants.
[1]
Question 30
Stability of a star and stability of a nucleus both involve competing effects.
State the dominant inward effect in a star.
[1]
Compare this with the interaction responsible for holding a nucleus together.
[1]
Question 31
Space telescopes can improve stellar parallax measurements.
State the baseline used in the simple definition of the parallax angle.
[1]
Explain why a space telescope can measure distances to more distant stars than a ground-based telescope.
[1]
Question 32
The HR diagram shows five labelled stars P, Q, R, S and T.
| Star | Surface temperature / K | Luminosity / L☉ |
|---|---|---|
| P | 20000 | 1000 |
| Q | 5800 | 1.0 |
| R | 30000 | 0.010 |
| S | 3900 | 500 |
| T | 3300 | 0.030 |
Identify the labelled star most likely to be a white dwarf.
[1]
Identify the labelled star most likely to be a red giant.
[1]
State which labelled star has the greatest surface temperature.
[1]
Explain why the red giant can have high luminosity despite a relatively low surface temperature.
[1]
Question 33
A table gives measurements for four stars: apparent brightness, distance and surface temperature.
| Star | Apparent brightness / W m⁻² | Distance / m | Surface temperature / K |
|---|---|---|---|
| A | 2.0 × 10⁻⁸ | 1.0 × 10¹⁷ | 5800 |
| B | 5.0 × 10⁻¹⁰ | 8.0 × 10¹⁷ | 4500 |
| C | 1.5 × 10⁻⁹ | 1.5 × 10¹⁸ | 7200 |
| D | 8.0 × 10⁻⁸ | 5.0 × 10¹⁶ | 11000 |
Identify the star with the greatest luminosity.
[1]
Calculate the luminosity of one specified star using the data.
[1]
Suggest why the radius determined from these data is only an estimate.
[1]
Question 34
The spectrum of a star is shown with a smooth black-body curve and several absorption lines.
Estimate the wavelength at which the intensity is maximum.
[1]
Use T = 2.90 × 10⁻³ / λmax to determine the surface temperature.
[1]
State one property of the star that can be inferred from the absorption lines.
[1]
Question 35
In a simplified fusion reaction, the decrease in rest mass is 4.6 × 10⁻²⁹ kg.
Calculate the energy released in joule. Use c = 3.00 × 10⁸ m s⁻¹.
[1]
Convert this energy to MeV. Use 1 MeV = 1.60 × 10⁻¹³ J.
[1]
Question 36
A star has apparent brightness 2.0 × 10⁻¹⁰ W m⁻² and is 5.0 × 10¹⁷ m from Earth.
Calculate its luminosity.
[1]
Outline how the star’s radius could then be determined if its surface temperature is known.
[1]
Question 37
Two stars A and B lie on an HR diagram. Star A has luminosity 100 L☉ and temperature 2T☉. Star B is the Sun.
Calculate the radius of star A in solar radii.
[1]
State whether A could be a white dwarf. Justify your answer.
[1]
Question 38
The table gives initial masses of several stars and model predictions for their luminosities, main-sequence lifetimes and final remnants.
| Model | Initial mass / M☉ | Luminosity / L☉ | Lifetime / 10^9 yr | Predicted remnant |
|---|---|---|---|---|
| A | 0.8 | 0.35 | 23 | white dwarf |
| B | 1.0 | 1.0 | 10 | white dwarf |
| C | 2.0 | 11 | 1.8 | white dwarf |
| D | 5.0 | 720 | 0.070 | white dwarf |
| E | 7.0 | 1900 | 0.037 | white dwarf |
| F | 8.0 | 3100 | 0.026 | WD or NS |
| G | 9.0 | 5200 | 0.017 | neutron star |
| H | 12.0 | 16000 | 0.0075 | neutron star |
| I | 20.0 | 95000 | 0.0021 | black hole |
Describe the trend between initial mass and main-sequence lifetime.
[1]
Explain why this trend occurs even though high-mass stars contain more fuel.
[1]
Evaluate whether the data support a sharp boundary between white-dwarf and neutron-star remnants.
[1]
Question 39
The graph shows luminosity against surface temperature for several stars. Lines of constant radius are also shown.
Identify the star with the largest radius.
[1]
Determine the radius of a specified star in solar radii using the constant-radius lines.
[1]
Calculate the radius of the same star using L/L☉ = (R/R☉)²(T/T☉)⁴.
[1]
Suggest why the graphical and calculated radii may differ slightly.
[1]
Question 40
The diagram shows possible final states for stellar remnants as a function of remnant mass.
| Remnant mass / M☉ | Possible final state | Marked boundary |
|---|---|---|
| < 1.4 | White dwarf | Chandrasekhar limit at 1.4 M☉ |
| 1.4–3.0 | Neutron star | Oppenheimer–Volkoff limit at 3.0 M☉ |
| > 3.0 | Black hole | Above O–V limit |
State the compact object expected below the Chandrasekhar limit.
[1]
Identify the mass range in which a neutron star is possible.
[1]
Explain the role of degeneracy pressure in the two labelled stable remnant regions.
[1]
Question 41
The figure shows an HR diagram for stars in a cluster, including a main sequence turn-off point and an instability strip.
Identify the region containing pulsating variable stars.
[1]
Describe how the main sequence differs above and below the turn-off point.
[1]
Explain why the turn-off point provides evidence about the age of the cluster.
[1]
Suggest one limitation of using a single HR diagram to predict future stellar evolution.
[1]
Question 42
A gas cloud contracts to form a stable main-sequence star.
Outline how contraction changes the temperature and density of the cloud.
[1]
Explain how a main-sequence star remains stable and why the gas-law model is useful but limited.
[1]
Question 43
The initial mass of a star strongly affects its evolution.
Describe two properties of a main-sequence star that depend on its initial mass.
[1]
Discuss the evolution of a moderate-mass star after it leaves the main sequence.
[1]
Question 44
Fusion and fission both release nuclear energy.
State the condition for a nuclear reaction to release energy in terms of binding energy.
[1]
Compare and contrast fusion in stars with nuclear fission as energy-releasing processes.
[1]
Question 45
A table gives nuclear masses for species in a simplified proton–proton-chain calculation.
| Species | Mass / u |
|---|---|
| proton | 1.007276 |
| helium-4 nucleus | 4.001506 |
| positron | 0.0005486 |
| neutrino | 0.0000000 |
Use the data to determine the mass defect for the overall conversion of four protons into one helium-4 nucleus and emitted particles.
[1]
Calculate the energy released in MeV. Use 1 u c² = 931.5 MeV.
[1]
Explain why the energy available to heat the star is less than the total calculated in (b).
[1]
Question 46
An astronomer uses a star’s spectrum, apparent brightness and parallax to determine the star’s radius.
State how each of the following is determined: distance from parallax; surface temperature from spectrum.
[1]
Evaluate the method used to determine the stellar radius from these observations.
[1]
Question 47
A high-mass star evolves beyond the main sequence and ends as a compact remnant.
Explain why a high-mass star has a shorter main-sequence lifetime than a low-mass star.
[1]
Explain the later evolution of a high-mass star, including the role of limiting masses for compact remnants.
[1]
Question 48
Solar neutrino measurements have been used as evidence for fusion in the Sun.
Outline the role of neutrinos in the proton–proton chain.
[1]
Evaluate why neutrino observations are powerful evidence for solar-core fusion and why their interpretation requires care.
[1]
Question 49
HR diagrams are used to classify stars and to test models of stellar evolution.
Outline the main regions of an HR diagram.
[1]
Discuss how HR diagrams, spectra and improved telescope technology contribute to our understanding of stellar evolution.
[1]
Question 50
A research team claims that a newly observed object is a red supergiant. They have measured its parallax, apparent brightness and spectrum.
Describe how the team can use the observations to determine luminosity and surface temperature.
[1]
Evaluate how the team could use these results to test the red-supergiant classification.
[1]
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