DP Physics Questionbank

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.

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.

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

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.

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.

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.

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

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.

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 $E=\frac{1}{2}m{v}^2-\frac{4}{3}\pi G\text{r}{r}^{2}m$.

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

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

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.