Red-shift & the expanding universe

A spectral line with wavelength 655.88 nm is detected on Earth from the Triangulum Galaxy. The wavelength of this spectral line measured using a laboratory source is 656.28 nm.

Calculate the velocity of the Triangulum Galaxy relative to the Earth.

A pulsar is a rotating neutron star. The pulsar emits electromagnetic radiation as it rotates.

Scientists have recently detected the highest ever energy gamma ray photons received from a pulsar.

The energy of one of these gamma ray photons was determined to be 2.0×10¹³eV.

Calculate the wavelength of these gamma rays.

The pulsar is estimated to be travelling away from the Earth with a velocity

State why this motion away from the Earth does not significantly affect the wavelength of radiation received at the Earth.

In 1864, William Huggins and William Miller used dark lines in the spectrum of the Sun to identify elements in the Sun’s atmosphere.

*(a) Explain how gases in the Sun’s atmosphere cause dark lines in the spectrum corresponding to different elements.

In 1868, William Huggins analysed light from the star Sirius A. The wavelength of the hydrogen-alpha line for light from Sirius A was slightly different from the hydrogen-alpha line observed from a source in a laboratory.

Huggins suggested that this difference could be explained using the Doppler effect and could be used to determine the speed and direction of the star’s motion relative to the Earth.

Assess Huggins’s suggestion.

Sirius A has a component of velocity away from the Earth of 5.5 km s^–1.

The wavelength of the hydrogen-alpha line observed from a source in the laboratory is 656.46 nm.

Calculate the wavelength of the hydrogen-alpha line as seen in the spectrum of Sirius A.

The photograph below was taken by the James Webb Space Telescope (JWST) and shows a group of galaxies that formed shortly after the big bang, about 1310⁹ years ago.

Derive the equation T = 1/H₀ where T is the age of the universe.

State one assumption made in your derivation.

The parsec (pc) is a unit used for astronomical distances. 1 pc is 3.1×10¹⁶m.

The accepted range for the Hubble constant H₀ is (60–80) km s^–1 Mpc^–1. Deduce whether the observation by the JWST leads to a value of H₀ within the accepted range.

1 year = 3.1610⁷s

The light from one of the galaxies, called Maisie, has a redshift z of 14. The wavelength of light from Maisie detected at the telescope is 4.010^–6m and lies within the infrared section of the electromagnetic spectrum.

Calculate the wavelength of light emitted by Maisie.

Explain why the light emitted by Maisie arrives at the telescope as infrared.

One of the infrared detectors on the JWST is made from material with a work function of 0.30 eV.

Deduce whether this detector can detect the light from Maisie.

Explain why the long wavelength lines are shifted by a greater amount than the short wavelength lines.

One of the lines in the hydrogen spectrum occurs at a wavelength of 656 nm in the laboratory.

Explain what conclusion can be made from the shift in wavelength of this line in spectrum B. Your answer should include a calculation.

Astronomers observing stars at the centre of our galaxy have suggested that many of them are orbiting a supermassive black hole. The mass of this black hole is 9.2 10³⁶kg.

Calculate the orbital period for a star in a circular orbit at a distance of 1.9 10¹⁴m from a black hole of this mass.

The star S0-2 is in a highly elliptical orbit around the position of the black hole.

At its point of closest approach, S0-2 is at a distance of 1.8 10¹³m from the centre of the black hole.

At the most distant point of its orbit, S0-2 is 2.7 10¹⁴m from the black hole.

Show that the change in gravitational potential between the closest and most distant points in this orbit is about 3 10¹³J kg⁻¹.

At its point of closest approach, the star is travelling at a speed of 8.1 10⁶m s⁻¹.

Calculate the speed of S0-2 at the furthest point in its orbit using the change in gravitational potential.

mass of S0-2 = 2.4 10³¹kg

Trigonometric parallax and Hubble’s law are two methods used to determine astronomical distances. Explain whether either of these methods is suitable to determine the distance to S0-2.

There are several different methods that can be used to determine the distance from our solar system to astronomical objects. These include the measurement of red shift, trigonometrical parallax and the use of standard candles.

Which row of the table shows a suitable method for each of the objects named?

There are several different methods that can be used to determine the distance from our solar system to astronomical objects. These include the measurement of red shift, trigonometrical parallax and the use of standard candles.

Which row of the table shows a suitable method for each of the objects named?

At the Culham Centre for Fusion Energy (CCFE) experiments are carried out to investigate nuclear fusion and the properties of plasmas. A plasma consists of ionised gas, containing positive ions and electrons.

In a fusion experiment at CCFE, ions of two isotopes of hydrogen fuse to produce helium ions and fast-moving neutrons.

Show that a single fusion reaction releases about 3 10⁻¹²J of energy.

mass of₁²H = 2.013553 u mass of₁³H = 3.015501 u mass of⁴₂He = 4.001506 u mass of₀¹n = 1.008665 u

Fusion occurs naturally in the core of stars.

Explain why very high densities of matter and very high temperatures are needed to bring about and maintain nuclear fusion in stars.

In a plasma experiment 5.0 mg of deuterium, an isotope of hydrogen, occupies a volume of 98 m³. The temperature of deuterium is raised to 1.3 10⁸K. In this experiment, the deuterium behaves as an ideal gas.

Calculate the pressure due to the deuterium ions.

mass of deuterium ion = 3.3 10⁻²⁷kg

Calculate the root mean square speed of the deuterium ions at this temperature.

The temperature of the plasma is monitored using the Doppler effect. Light from a laser is directed into the plasma and the wavelength of the light reflected is measured.

The Doppler shift observed when light is reflected by a deuterium ion is twice the Doppler shift that would be observed for a source of light moving at the same speed as the deuterium ion.

Calculate the maximum wavelength of light that would be detected after reflection from a deuterium ion moving at 1.5 × 10⁶m s⁻¹.

wavelength of laser light = 1064 nm

At the Culham Centre for Fusion Energy (CCFE) experiments are carried out to investigate nuclear fusion and the properties of plasmas. A plasma consists of ionised gas, containing positive ions and electrons.

Fusion occurs naturally in the core of stars.

Explain why very high densities of matter and very high temperatures are needed to bring about and maintain nuclear fusion in stars.

In a plasma experiment 5.0 mg of deuterium, an isotope of hydrogen, occupies a volume of 98 m³. The temperature of deuterium is raised to 1.3 10⁸K. In this experiment, the deuterium behaves as an ideal gas.

Calculate the pressure due to the deuterium ions.

mass of deuterium ion = 3.3 10⁻²⁷kg

Calculate the root mean square speed of the deuterium ions at this temperature.

The temperature of the plasma is monitored using the Doppler effect. Light from a laser is directed into the plasma and the wavelength of the light reflected is measured.

The Doppler shift observed when light is reflected by a deuterium ion is twice the Doppler shift that would be observed for a source of light moving at the same speed as the deuterium ion.

Calculate the maximum wavelength of light that would be detected after reflection from a deuterium ion moving at 1.5 × 10⁶m s⁻¹.

wavelength of laser light = 1064 nm

In 1990, the Hubble Space Telescope (HST) was launched into a low Earth orbit above the Earth’s atmosphere.

HST orbits the Earth in a circular orbit with a speed of 7.59 km s^–1.

mass of Earth = 5.97 × 10²⁴ kg radius of Earth = 6.37 10⁶ m

Show that the height of HST above the surface of the Earth is about 6 × 10⁵ m.

Calculate the increase in the gravitational potential energy as HST is raised, from its initial position at the Earth’s surface, to its orbital height.

mass of HST = 11 600 kg

A student suggests that giving HST more energy than that required in (ii) would result in the satellite orbiting at a greater height and with a greater speed.

Assess the validity of the student’s suggestion.

The transmission of electromagnetic radiation through the atmosphere is shown on the graph.

State one advantage shown by this graph of positioning a telescope above the atmosphere.

High resolution images from HST allow astronomers to make detailed measurements of very distant galaxies. The graph shows how the recessional velocities of distant galaxies depend on their distance from Earth.

Determine an age for the universe.

A line in the hydrogen spectrum of a star in the Milky Way galaxy is observed to have a wavelength of 656.3 nm. In a laboratory on Earth this line has a wavelength of 654.9 nm.

Which of the following expressions gives the magnitude of the velocity of the star relative to Earth?

The distance to astronomical objects relatively close to the Sun is determined using trigonometric parallax. For objects beyond a certain distance standard candles are used.

State what is meant by a standard candle.

Explain why trigonometric parallax is not used beyond a certain distance.

Describe how distances too large for the use of standard candles can be determined.

Barnard’s star is a red dwarf star in the vicinity of the Sun. The wavelength of a line in the spectrum of light emitted from Barnard’s star is measured to be 656.0 nm. The same light produced by a source in a laboratory has a wavelength of 656.2 nm.

Calculate the velocity of Barnard’s star relative to the Earth.

A diffraction grating can be used to analyse the radiation emitted by a variety of sources.

A diffraction grating of known grating spacing is used in a school laboratory to analyse the light emitted by a laser.

Describe how the diffraction grating is used and the measurements that should be taken.

A diffraction grating with grating spacing of 2.2 × 10⁻⁶ m is used to determine the difference in wavelength for the spectral line emitted by Barnard’s star.

Comment on the suitability of using a diffraction grating with this spacing. You should include appropriate calculations.

Visible light from the star originates from the photosphere. In the photosphere of Barnard’s star, hydrogen and helium atoms are at a temperature of 3100 K.

Calculate the mean kinetic energy of an atom in the photosphere at a temperature of 3100 K.

Describe how these atoms emit visible light.