Question 1
A main-sequence star remains at approximately constant radius for a long period of time. What condition is required for this stability?
A.
Outward nuclear pressure balances inward electric pressure
B.
Outward gravitational pressure balances inward radiation pressure
C.
Outward thermal or radiation pressure balances inward gravitational pressure
D.
Outward electric pressure balances inward nuclear pressure
Question 2
The core of a protostar must reach particular conditions before sustained hydrogen fusion begins. Which pair of conditions is required?
A.
Low temperature and high density
B.
High temperature and high density
C.
Low temperature and low density
D.
High temperature and low density
Question 3
In one completed proton-proton chain, the decrease in rest mass is . The energy equivalent of is . What is the energy released?
A.
B.
C.
D.
Question 4
The diagram is a Hertzsprung-Russell diagram with four labelled stars. Temperature increases to the left. Which labelled star is most likely to be a white dwarf?
A.
The star near the middle of the main sequence
B.
The star in the lower left region
C.
The star in the upper right region
D.
The star in the lower right region
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Question 5
A nearby star has a stellar parallax angle of arcsecond. What is its distance from Earth?
A.
B.
C.
D.
Question 6
The first stage of the proton-proton chain is
What feature of this stage explains why the proton-proton chain is slow in Sun-like stars?
A.
An electron must be absorbed to produce a gamma photon
B.
A helium nucleus must split before deuterium can form
C.
A neutron must change into a proton through the strong interaction
D.
A proton must change into a neutron through the weak interaction
Question 7
A stellar remnant has mass greater than the Chandrasekhar limit. What statement is correct?
A.
It cannot remain a stable white dwarf supported by electron degeneracy pressure
B.
It must stop radiating because fusion has ended
C.
It must immediately become a main-sequence star
D.
It can remain a stable white dwarf supported by electron degeneracy pressure
Question 8
A main-sequence star remains approximately the same size for a long period of time.
State the condition for hydrostatic equilibrium in the star.
[1]
Explain why contraction of a gas cloud can increase the pressure in its core.
[2]
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Question 9
Hydrogen fusion begins in the core of a protostar only after the core has changed sufficiently.
Outline two core conditions required for sustained fusion.
[2]
State why high temperature helps hydrogen nuclei to fuse.
[1]
Question 10
A star has luminosity and surface temperature , where and are the luminosity and surface temperature of the Sun. What is the radius of the star in terms of the solar radius ?
A.
B.
C.
D.
Question 11
The graph shows binding energy per nucleon against nucleon number. A reaction combines two light nuclei to form a product nucleus closer to the peak of the curve. What conclusion follows?
A.
Energy is released because the product has greater binding energy per nucleon
B.
Energy is released because the product has lower binding energy per nucleon
C.
Energy is absorbed because the product has greater binding energy per nucleon
D.
Energy is absorbed because the nucleon number always decreases in fusion
Question 12
A compact stellar remnant is made mainly of neutrons. Its mass is above the Oppenheimer-Volkoff limit. What is its expected final state?
A.
A red giant
B.
A black hole
C.
A stable neutron star
D.
A white dwarf
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Question 13
A high-mass star has formed an iron-rich core after successive stages of nuclear fusion. Why does further fusion in the core not provide a useful source of energy to support the star?
A.
Iron fusion releases only chemical energy rather than nuclear energy
B.
Iron nuclei have no protons and cannot undergo electric repulsion
C.
Iron nuclei are too cold to emit neutrinos
D.
Iron-group nuclei are near the maximum binding energy per nucleon
Question 14
One stage of the proton-proton chain is
The following atomic masses are available.
Use .
Calculate the energy released in this reaction in MeV.
[3]
Outline why this reaction releases energy.
[1]
Question 15
The figure shows an unlabelled Hertzsprung-Russell diagram.
On the HR diagram, label the main sequence, the red giant region and the white dwarf region.
[3]
State the unusual feature of the temperature axis on an IB-style HR diagram.
[1]
Question 16
A nearby star has a measured parallax angle of arcsecond.
Calculate the distance to the star in parsecs.
[1]
Convert this distance to light years. Use .
[1]
State the effect on the calculated distance if the measured parallax angle is smaller.
[1]
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Question 17
The graph shows a model of pressure inside a stable main-sequence star. The radius is shown as a fraction of the stellar radius.
State the region of the star where the total pressure is greatest.
[1]
Describe how the relative importance of radiation pressure changes from the centre to the surface.
[1]
Explain why a stable star does not collapse under its own gravity.
[2]
Question 18
A computer model predicts the relative fusion rate in a cloud of ionized hydrogen for different core temperatures and densities.
State the effect of increasing density at a fixed temperature on the predicted fusion rate.
[1]
Outline why high temperature is needed for fusion of hydrogen nuclei.
[1]
Explain why a contracting protostar may become a main-sequence star only after both temperature and density are sufficiently high.
[2]
Question 19
Two stars lie on the same constant-radius line of a Hertzsprung-Russell diagram. Star X has twice the surface temperature of star Y. What is the luminosity of star X compared with star Y?
A.
B.
C.
D.
Question 20
A star has luminosity and surface temperature . Take the surface temperature of the Sun to be .
Calculate the radius of the star in units of the solar radius .
[3]
Suggest the likely region of the HR diagram occupied by this star.
[1]
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Question 21
Gas laws are often used as a first model for matter inside stars.
Explain one way in which a gas-law model helps to describe stellar stability.
[2]
Discuss one limitation of treating a star as an ideal gas.
[2]
Question 22
The first step in the proton-proton chain is very slow compared with most nuclear collision processes.
Complete the nuclear equation for the first step of the proton-proton chain.
[2]
Explain why this step is slow and why solar neutrinos provide evidence for fusion in the Sun.
[2]
Question 23
The figure shows the general variation of binding energy per nucleon with nucleon number.
Compare the energy release in fusion of light nuclei with fission of heavy nuclei using the graph.
[2]
Distinguish between photons emitted in atomic transitions and photons emitted in nuclear transitions.
[2]
Question 24
A high-mass star has exhausted hydrogen in its core and has formed an iron-rich core near the end of its life.
Explain why fusion reactions beyond the iron region do not provide a further source of energy for the star.
[2]
Discuss the possible final remnant after the core collapses.
[2]
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Question 25
The table gives rest masses that may be used for the overall proton-proton chain reaction in a Sun-like star.
Use .
Atom | Atomic mass / u |
|---|---|
¹H atom | 1.007825 |
⁴He atom | 4.002603 |
Determine the mass decrease for one completed production of a helium nucleus, using the atomic masses in the table.
[2]
Calculate the energy released, in MeV, for this reaction.
[1]
Explain why detecting neutrinos from the Sun provides evidence that fusion occurs in the solar core.
[2]
Question 26
The table compares four main-sequence stars formed from the same type of gas cloud.
Star | Initial mass / | Luminosity / | Main-sequence lifetime / Gyr |
|---|---|---|---|
A | 0.8 | 0.4 | 20 |
B | 1.0 | 1.0 | 10 |
C | 2.0 | 20 | 1.0 |
D | 5.0 | 1000 | 0.1 |
Identify the star that will spend the shortest time on the main sequence.
[1]
Using the data, describe the relationship between initial mass and main-sequence lifetime.
[1]
Explain why the most massive star has a shorter lifetime even though it contains more hydrogen fuel.
[2]
State the main source of energy of a main-sequence star.
[1]
Question 27
The diagram is an H-R diagram for a group of nearby stars. Temperature increases to the left.
Star | Temperature / K | Luminosity / |
|---|---|---|
A | 20000 | 0.001 |
B | 10000 | 20 |
E | 6000 | 1.0 |
D | 4000 | 0.03 |
C | 4000 | 300 |
Identify the labelled star most likely to be a white dwarf.
[1]
Compare the radius of the red giant with that of a main-sequence star of the same surface temperature shown on the diagram.
[1]
Use to explain why a white dwarf can be hot but have a low luminosity.
[2]
Question 28
A star has apparent brightness and parallax angle arcsecond. Its surface temperature is .
Use , and .
Determine the distance to the star in metres.
[1]
Calculate the luminosity of the star.
[2]
Estimate the radius of the star in units of .
[1]
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Question 29
The figure shows blank axes for an HR diagram. Luminosity is plotted vertically and surface temperature increases to the left.
Sketch a line of constant stellar radius on the HR diagram.
[2]
Mark the approximate position of the instability strip on the same axes.
[1]
Use the Stefan-Boltzmann law to justify the direction of the constant-radius line.
[1]
Question 30
Observations of one star are shown. Use , and .
Observed quantity / unit | Value |
|---|---|
Parallax, / arcsec | 0.050 |
Bolometric flux, / W m | |
Peak wavelength, / m |
Calculate the distance to the star in parsecs.
[1]
Calculate the luminosity of the star in solar luminosities using .
[2]
Use the spectrum and the result from (b) to determine the radius of the star in solar radii.
[2]
Question 31
The graph shows binding energy per nucleon for light nuclei. The values for hydrogen and helium isotopes are highlighted.
Determine the total binding energy of one helium-4 nucleus from the graph.
[1]
Explain why energy is released when four hydrogen nuclei form one helium-4 nucleus.
[2]
The energy available to heat the star is less than the total energy released. Suggest why.
[2]
Question 32
An H-R diagram for a cluster is shown. The diagram includes lines of constant radius and an instability strip.
Identify the labelled star most likely to show periodic luminosity variations associated with pulsation.
[1]
Star P has and . Determine its radius in solar radii. Use .
[2]
Suggest one reason why stars in the same region of an H-R diagram may still have different compositions.
[1]
Explain why the temperature axis on the diagram is useful even though it runs in the opposite direction to many graphs.
[1]
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Question 33
The diagram summarizes possible final states of stellar cores after the outer layers of a star have been lost or expelled.
State the predicted remnant for a core of mass .
[1]
State the predicted remnant for a core mass above the Oppenheimer-Volkoff limit.
[1]
Explain why a white dwarf has a maximum stable mass.
[2]
Question 34
The spectrum of a star is shown together with laboratory wavelengths of absorption lines for two elements.
The spectrum peaks at . Determine the surface temperature of the star using .
[1]
State how the spectrum can be used to infer the chemical composition of the star's outer layers.
[1]
Explain why photons from the absorption lines and photons from nuclear transitions are the same type of particle but usually have different energies.
[2]
Question 35
A newly formed star is observed to have a nearly constant radius while hydrogen fusion takes place in its core.
The star is in hydrostatic equilibrium.
I.
Explain what is meant by hydrostatic equilibrium in this star.
[2]
II.
Explain why both thermal pressure and radiation pressure can contribute to the outward pressure.
[2]
The rate of fusion in the core decreases as hydrogen fuel becomes depleted. Discuss the likely sequence of changes in the star immediately after this decrease.
[3]
Question 36
Two protostars form in the same gas cloud. Star X has initial mass and star Y has initial mass .
Compare the early main-sequence properties of stars X and Y.
I.
Explain why star Y reaches a higher core temperature than star X.
[2]
II.
Explain why star Y has a shorter main-sequence lifetime although it contains more hydrogen fuel.
[2]
Discuss the expected final stages of evolution of stars X and Y.
[4]
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Question 37
A proposed fusion reactor on Earth is designed to use the deuterium-tritium reaction, while stars such as the Sun mainly use hydrogen fusion in their cores.
Fusion can occur only under extreme conditions.
I.
Explain why high temperature is required for fusion of light nuclei.
[2]
II.
Explain why high density is also required in a stellar core.
[2]
Discuss one advantage and two difficulties of obtaining useful energy from fusion on Earth.
[3]
Question 38
Two types of solar-neutrino detector measured the neutrino flux from the Sun. Detector X is sensitive mainly to electron neutrinos. Detector Y is sensitive to all neutrino types.
Source | Flux / | Unc. / |
|---|---|---|
Predicted solar model | 6.0 | — |
Detector X | 1.9 | 0.2 |
Detector Y | 5.8 | 0.5 |
Compare the measured fluxes from detector X and detector Y with the predicted solar-model flux.
[2]
Explain how the data support the conclusion that fusion occurs in the solar core.
[1]
Evaluate whether the data support the idea that electron neutrinos change type during their journey from the Sun to Earth.
[2]
Question 39
A space telescope measures the parallax of several stars. A second method uses a standard candle in the same region of space.
Object | Parallax / arcsec | Apparent brightness / W m | Standard-candle luminosity / W |
|---|---|---|---|
A | 0.020 | — | |
B | 0.010 | — | |
C | 0.002 |
Object A has a parallax angle of arcseconds. Calculate its distance in parsecs and in light years. Use .
[2]
Suggest why the parallax distance for the most distant object is less reliable than for object A.
[1]
Evaluate why the standard-candle method can be useful even when parallax data are available.
[2]
Question 40
In the proton-proton chain, four hydrogen nuclei are converted into one helium nucleus. The total energy released per completed helium nucleus is about .
A model of a Sun-like star assumes that helium nuclei are produced each second.
I.
Calculate the energy released per completed helium nucleus in joules.
[2]
II.
Assuming helium nuclei are produced each second, estimate the luminosity of the star due to this fusion.
[2]
III.
Suggest why the measured photon luminosity would be smaller than the value calculated from the total fusion energy.
[1]
Explain why the first stage of the proton-proton chain is slow, and why this slow rate is important for the lifetime of Sun-like stars.
[3]
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Question 41
The positions of three stars, A, B and C, are shown on a Hertzsprung-Russell diagram.
Use the HR diagram to compare the likely physical properties of stars A, B and C.
I.
Explain why star A is expected to have a shorter main-sequence lifetime than the Sun.
[2]
II.
Explain why star C can be hot but have a low luminosity.
[2]
Star B has luminosity and surface temperature . Take . Evaluate whether star B is more likely to be a red giant or a main-sequence star.
[4]
Question 42
A nearby star has parallax angle and apparent brightness . Use .
The parallax measurement is used to determine the distance to the star.
I.
Calculate the distance to the star in parsecs.
[1]
II.
Calculate the distance to the star in metres.
[1]
III.
Determine the luminosity of the star.
[2]
Evaluate the reliability of using parallax and apparent brightness to determine stellar radius for this star.
[4]
Question 43
Solar neutrino detectors observe particles produced in the core of the Sun. Early experiments detected fewer electron neutrinos than predicted by solar models.
The first stage of the proton-proton chain is
I.
In the reaction , use conservation laws to explain why a neutrino is emitted.
[2]
II.
Explain why solar neutrinos provide direct evidence for fusion in the Sun's core.
[2]
Discuss how the historical deficit of detected electron neutrinos illustrates the interaction between observation and physical models.
[3]
Question 44
Both a star and an atomic nucleus can be described as stable systems, but the physics responsible for their stability is different.
A simplified gas model is used to describe the interior of a star.
I.
Explain why gas laws can be useful in modelling a star.
[2]
II.
Explain one limitation of treating a star as an ideal gas.
[2]
Compare and contrast the equilibrium of a star with the stability of a nucleus.
[3]
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Question 45
The graph shows how nuclear binding energy per nucleon varies with nucleon number. It is used to interpret fusion in stars.
Use the binding energy curve to explain energy release in stellar fusion.
I.
Explain why fusion of hydrogen into helium releases energy.
[2]
II.
Explain why fusion reactions beyond the iron-group nuclei do not provide a useful energy source for a star.
[2]
A high-mass star develops an onion-like shell structure late in its life. Evaluate how this structure affects the final collapse of the star.
[4]
Question 46
A star in a nearby galaxy is used as a standard candle. Its known luminosity is and its measured apparent brightness is . Its spectrum has peak wavelength . Use for Wien's displacement constant.
The apparent brightness and spectrum are used to infer physical properties of the star.
I.
Calculate the distance to the star.
[2]
II.
Determine the surface temperature of the star.
[1]
III.
Describe how the same spectrum can give information about the composition of the star.
[2]
Evaluate the use of this standard candle method compared with stellar parallax for determining distances to stars in a nearby galaxy.
[3]
Question 47
Three stellar remnants have masses , and . The Chandrasekhar limit is about and the Oppenheimer-Volkoff limit is of order to .
Use the limiting masses to predict the nature of each remnant.
I.
Identify the most likely remnant for the object and explain the pressure supporting it.
[2]
II.
Identify the most likely remnant for the object and explain the pressure supporting it.
[2]
Evaluate the likely fate of the remnant and the role of degeneracy pressure in this fate.
[4]
Question 48
An HR diagram for an open star cluster contains a main sequence that bends away at high luminosity. The cluster also contains several red giants and white dwarfs.
Interpret the pattern of stars in the HR diagram.
I.
Explain why the absence of the most luminous upper-main-sequence stars gives information about the age of the cluster.
[2]
II.
Explain why red giants and white dwarfs can both be present in the same cluster.
[2]
Evaluate how HR diagrams allow astronomers to make predictions about stellar evolution, and state one limitation of these predictions.
[4]
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