DP Physics Questionbank

A standard Hertzsprung–Russell (HR) diagram is shown.

Using the HR diagram, draw the present position of Alpha Centauri A and its expected evolutionary path.

Calculate the rotation velocity of stars 4.0 kpc from the centre of the galaxy. The average density of the galaxy is 5.0 × 10^–21 kg m^–3.

(i) Calculate $\frac{b_{\text{A}}}{b_{\text{B}}}=\frac{\text{apparent brightness of Alpha Centauri A}}{\text{apparent brightness of Alpha Centauri B}}$.

(ii) The luminosity of the Sun is 3.8 × 10²⁶ W. Calculate the radius of Alpha Centauri A.

Determine the distance from Earth to the Cepheid star in parsecs. The luminosity of the Sun is 3.8 × 10²⁶ W. The average apparent brightness of the Cepheid star is 1.1 × 10^–9 W m^–2.

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

Determine the distance of Theta 1 Orionis in AU.

Estimate the size of the Universe relative to its present size when the light was emitted by the galaxy in (c).

State what is meant by a main sequence star.

State two characteristics of the cosmic microwave background (CMB) radiation.

Determine the distance to this galaxy using a value for the Hubble constant of H₀ = 68 km s^–1$$Mpc^–1.

The present temperature of the CMB is 2.8 K. Calculate the peak wavelength of the CMB.

Show that the mass of Theta 1 Orionis is about 40 solar masses.

Discuss how Theta 1 Orionis does not collapse under its own weight.

Describe how the CMB provides evidence for the Hot Big Bang model of the universe.

The surface temperature of the Sun is about 6000 K. Estimate the surface temperature of Theta 1 Orionis.

The Sun and Theta 1 Orionis will eventually leave the main sequence. Compare and contrast the different stages in the evolution of the two stars.

The Hertzsprung–Russell (HR) diagram shows two main sequence stars X and Y and includes lines of constant radius. R is the radius of the Sun.

Using the mass–luminosity relation and information from the graph, determine the ratio $\frac{\text{density of star X}}{\text{density of star Y}}$.

The radius of a typical neutron star is 20 km and its surface temperature is 10⁶ K. Determine the luminosity of this neutron star.

State the most abundant element in the core and the most abundant element in the outer layer.

Determine the region of the electromagnetic spectrum in which the neutron star in (c)(iii) emits most of its energy.

State two features of the cosmic microwave background (CMB) radiation which are consistent with the Big Bang model.

Describe what is meant by the Big Bang model of the universe.

Outline why the neutron star that is left after the supernova stage does not collapse under the action of gravitation.

On the HR diagram in (b), draw a line to indicate the evolutionary path of star X.

Describe how type Ia supernovae could be used to measure the distance to this galaxy.

Determine the distance to the galaxy in Mpc.

The graph shows the variation with time t of the cosmic scale factor R in the flat model of the universe in which dark energy is ignored.

On the axes above draw a graph to show the variation of R with time, when dark energy is present.

The density of dark energy is ρ_Λc² where ρ_Λ = ρ_c – ρ_m. Calculate the amount of dark energy in 1 m³ of space.

Describe what is meant by dark matter.

Outline, with reference to star formation, what is meant by the Jeans criterion.

In the proton–proton cycle, four hydrogen nuclei fuse to produce one nucleus of helium releasing a total of 4.3 × 10^–12 J of energy. The Sun will spend 10¹⁰ years on the main sequence. It may be assumed that during this time the Sun maintains a constant luminosity of 3.8 × 10²⁶ W.

Show that the total mass of hydrogen that is converted into helium while the Sun is on the main sequence is 2 × 10²⁹ kg.

Massive stars that have left the main sequence have a layered structure with different chemical elements in different layers. Discuss this structure by reference to the nuclear reactions taking place in such stars.

The present temperature of the CMB is 2.8 K. This radiation was emitted when the universe was smaller by a factor of 1100. Estimate the temperature of the CMB at the time of its emission.

State how the anisotropies in the CMB distribution are interpreted.

Curve A shows the actual rotation curve of a nearby galaxy. Curve B shows the predicted rotation curve based on the visible stars in the galaxy.

Explain how curve A provides evidence for dark matter.

The density of the observable matter in the universe is only 0.05 ρ_c. Suggest how the remaining 0.27 ρ_c is accounted for.

Derive, using the concept of the cosmological origin of redshift, the relation

T $\propto \frac{1}{R}$

between the temperature T of the cosmic microwave background (CMB) radiation and the cosmic scale factor R.

The distribution of mass in a spherical system is such that the density ρ varies with distance r from the centre as

ρ = $\frac{k}{r^2}$

where k is a constant.

Show that the rotation curve of this system is described by

v = constant.

Show by calculation that Eta Aquilae A is not on the main sequence.

Outline how Hubble’s law is related to $z$.

Show that the apparent brightness $b\propto \frac{A{T}^4}{d^2}$, where $d$ is the distance of the object from Earth, $T$ is the surface temperature of the object and $A$ is the surface area of the object.

The light from a distant galaxy shows that $z=0.11$.

Calculate the ratio $\frac{\mathrm{size} \mathrm{of} \mathrm{the} \mathrm{universe} \mathrm{when} \mathrm{the} \mathrm{light} \mathrm{was} \mathrm{emitted}}{\mathrm{size} \mathrm{of} \mathrm{the} \mathrm{universe} \mathrm{at} \mathrm{present}}$.

The astronomical unit ($\mathrm{AU}$) and light year ($\mathrm{ly}$) are convenient measures of distance in astrophysics. Define each unit.

$\mathrm{AU}$:

$\mathrm{ly}$:

Two of the brightest objects in the night sky seen from Earth are the planet Venus and the star Sirius. Explain why the equation $b\propto \frac{A{T}^4}{d^2}$ is applicable to Sirius but not to Venus.

Estimate, in $\text{pc}$, the distance to Eta Aquilae A using the parallax angle in the table.

Outline how Hubble’s law is related to $z$.

Estimate, in $\text{pc}$, the distance to Eta Aquilae A using the luminosity in the table, given that $L_{\odot }=3.83\times {10}^{26} \mathrm{W}$.

Estimate, in $\text{pc}$, the distance to Eta Aquilae A using the luminosity in the table, given that $L_{\odot }=3.83\times {10}^{26} \mathrm{W}$.

Estimate, in $\mathrm{pc}$, the distance to Eta Aquilae A using the parallax angle in the table.

Identify two possible causes of the anisotropies in (a).

The light from a distant galaxy shows that $z=0.11$.

Calculate the ratio $\frac{\mathrm{size} \mathrm{of} \mathrm{the} \mathrm{universe} \mathrm{when} \mathrm{the} \mathrm{light} \mathrm{was} \mathrm{emitted}}{\mathrm{size} \mathrm{of} \mathrm{the} \mathrm{universe} \mathrm{at} \mathrm{present}}$.

Show by calculation that Eta Aquilae A is not on the main sequence.

The Sun is a second generation star. Outline, with reference to the Jeans criterion (M_J), how the Sun is likely to have been formed.

Show that the critical density of the universe is

$$\frac{3H^2}{8\pi G}$$

where H is the Hubble parameter and G is the gravitational constant.

Suggest how fluctuations in the cosmic microwave background (CMB) radiation are linked to the observation that galaxies collide.

Determine the velocity of the galaxy relative to Earth.

Determine the radius of Sirius B in terms of the radius of the Sun.

The mass of visible matter in the galaxy is M.

Show that for stars where r > R₀ the velocity of orbit is v = $\sqrt{\frac{GM}{r}}$.

Describe the formation of a type Ia supernova.

Explain, using the equation in (a) and the graphs, why the presence of visible matter alone cannot account for the velocity of stars when r > R₀.

Show that the distance to the supernova is approximately 3.1 × 10¹⁸ m.

Draw on the axes the observed variation with r of the orbital speed v of stars in a galaxy.

State one assumption made in your calculation.

Outline, with reference to the Jeans criterion, why a cold dense gas cloud is more likely to form new stars than a hot diffuse gas cloud.

Explain how neutron capture can produce elements with an atomic number greater than iron.

Explain the evidence that indicates the location of dark matter in galaxies.

Outline why a hypothesis of dark energy has been developed.

plot the position, using the letter P, of the main sequence star P you calculated in (b).

plot the position, using the letter G, of Gacrux.

The luminosity of the Sun L${}_{\odot }$ is 3.85 × 10²⁶ W. Determine the luminosity of Gacrux relative to the Sun.

The distance to Gacrux can be determined using stellar parallax. Outline why this method is not suitable for all stars.

Estimate, using the data, the age of the universe. Give your answer in seconds.

Main sequence stars are in equilibrium under the action of forces. Outline how this equilibrium is achieved.

Discuss, with reference to its change in mass, the evolution of star P from the main sequence until its final stable phase.

A main sequence star P, is 1.3 times the mass of the Sun. Calculate the luminosity of P relative to the Sun.

draw the main sequence.

Identify the assumption that you made in your answer to (a).

On the graph, one galaxy is labelled A. Determine the size of the universe, relative to its present size, when light from the galaxy labelled A was emitted.

Distinguish between the solar system and a galaxy.

Distinguish between a planet and a comet. 

Suggest, using the graphs, why star X is most likely to be a main sequence star.

Show that the temperature of star X is approximately 10 000 K.

Write down the luminosity of star X (L_X) in terms of the luminosity of the Sun (L_s).

Determine the radius of star X (R_X) in terms of the radius of the Sun (R_s).

Estimate the mass of star X (M_X) in terms of the mass of the Sun (M_s).

Star X is likely to evolve into a stable white dwarf star.

Outline why the radius of a white dwarf star reaches a stable value.

Explain how international collaboration has helped to refine this value.

Estimate, in Mpc, the distance between the galaxy and the Earth.

Epsilon Indi is a main sequence star. Show that the mass of Epsilon Indi is 0.64 $M_{\odot }$.

Determine the peak wavelength of the radiation emitted by Epsilon Indi.

Use the graph to determine the age of the universe in s.

Outline how Hubble measured the recessional velocities of galaxies.

The following data are available for the Sun.

Surface temperature  = 5800 K

Luminosity                  = $L_{\odot }$

Mass                          = $M_{\odot }$

Radius                       = $R_{\odot }$

Epsilon Indi has a radius of 0.73 $R_{\odot }$. Show that the luminosity of Epsilon Indi is 0.2 $L_{\odot }$.

Determine the peak wavelength of the radiation emitted by Epsilon Indi.

The present temperature of the cosmic microwave background (CMB) radiation is 3 K. Estimate the size of the universe relative to the present size of the universe when the temperature of the CMB was 300 K.

Using the graph, determine in s, the age of the universe.

Outline how Hubble measured the recessional velocities of galaxies.

Epsilon Indi is a main sequence star. Show that the mass of Epsilon Indi is 0.64 $M_{\odot }$.

The following data are available for the Sun.

Surface temperature  = 5800 K

Luminosity                  = $L_{\odot }$

Mass                          = $M_{\odot }$

Radius                       = $R_{\odot }$

Epsilon Indi has a radius of 0.73 $R_{\odot }$. Show that the luminosity of Epsilon Indi is 0.2 $L_{\odot }$.

Show that the temperature of the universe is inversely proportional to the cosmic scale factor.

The Sun will spend about nine billion years on the main sequence. Calculate how long Epsilon Indi will spend on the main sequence.

A line in the hydrogen spectrum when measured on Earth has a wavelength of 486 nm. Calculate, in nm, the wavelength of the same hydrogen line when observed in the galaxy’s emission spectrum.

Determine the peak apparent brightness of δ-Cephei as observed from Earth.

Calculate the peak surface temperature of δ-Cephei.

Outline why the Sun will maintain a constant radius after it becomes a white dwarf.

Compare and contrast, the variation with time of the temperature of the cosmic background (CMB) radiation, for the two models from the present time onward.

Describe the mechanism of formation of type II supernovae.

During its evolution, the Sun is likely to be a red giant of surface temperature 3000 K and luminosity 10⁴ L_☉. Later it is likely to be a white dwarf of surface temperature 10 000 K and luminosity 10-4 L_☉. Calculate the $\frac{\text{radius of the Sun as a white dwarf}}{\text{radius of the Sun as a red giant}}$.

At critical density there is zero total energy. Show that the critical density of the universe is: ${\text{r}}_c=\frac{3H_0^2}{8\pi G}$.

Justify that the total energy of this particle is $E=\frac{1}{2}m{v}^2-\frac{4}{3}\pi G\text{r}{r}^{2}m$.

The mass of Sirius B is about the same mass as the Sun. The luminosity of Sirius B is 2.5 % of the luminosity of the Sun. Show, with a calculation, that Sirius B is not a main sequence star.

The peak spectral line of Sirius B has a measured wavelength of 115 nm. Show that the surface temperature of Sirius B is about 25 000 K.

The surface temperature of Eta Cassiopeiae B is 4100 K. Determine the ratio $\frac{\mathrm{radius} \mathrm{of} \mathrm{the} \mathrm{Eta} \mathrm{Cassiopeiae} \mathrm{A}}{\mathrm{radius} \mathrm{of} \mathrm{the} \mathrm{Eta} \mathrm{Cassiopeiae} \mathrm{B}}$.

Calculate the ratio $\frac{\mathrm{mass} \mathrm{of} \mathrm{Eta} \mathrm{Cassiopeiae} \mathrm{A}}{\mathrm{mass} \mathrm{of} \mathrm{the} \mathrm{Sun}}$.

The peak wavelength of radiation from Eta Cassiopeiae A is 490 nm. Show that the surface temperature of Eta Cassiopeiae A is about 6000 K.

Estimate the age of the universe in seconds using the Hubble constant H₀ = 70 km s^–1Mpc^–1.

Deduce the final evolutionary state of Eta Cassiopeiae A.

The distance of the Eta Cassiopeiae system from the Earth is 1.8 × 10¹⁷m. Calculate, in terms of $L_{\odot }$, the luminosity of Eta Cassiopeiae A.

Outline why the estimate made in (b)(i) is unlikely to be the actual age of the universe.

Light from a hydrogen source in a laboratory on Earth contains a spectral line of wavelength 122 nm. Light from the same spectral line reaching Earth from a distant galaxy has a wavelength of 392 nm. Determine the ratio of the present size of the universe to the size of the universe when the light was emitted by the galaxy.

Proxima Centauri is a main sequence star with a mass of 0.12 solar masses.

Estimate $\frac{\mathrm{lifetime} \mathrm{on} \mathrm{main} \mathrm{sequence} \mathrm{of} \mathrm{Proxima} \mathrm{Centauri}}{\mathrm{lifetime} \mathrm{on} \mathrm{main} \mathrm{sequence} \mathrm{of} \mathrm{Sun}}$.

Light from a hydrogen source in a laboratory on Earth contains a spectral line of wavelength 122 nm. Light from the same spectral line reaching Earth from a distant galaxy has a wavelength of 392 nm. Determine the ratio of the present size of the universe to the size of the universe when the light was emitted by the galaxy.

Calculate the density of matter in the universe, using the Hubble constant 70 km s^–1Mpc^–1.

Discuss one process by which elements heavier than iron are formed in stars.