The Doppler effect

Calculate the magnitude of the recession velocity of M87.

velocity =........ km s^–1

Estimate the distance in light years to M87 using Hubble’s law.

Hubbles constant H_o = 2.5 × 10^–19 s^–1

Estimate the percentage uncertainty in the distance calculated in part (b) using the width of the emission line in the diagram.

percentage uncertainty = +/–........ %

Other methods have shown M87 is actually 50 million light years from Earth.

Suggest why M87 might contradict Hubble’s law.

Suggest one reason why the Big Bang theory is still the accepted model of the origin of the Universe.

Part of the emission spectrum for hydrogen in a laboratory is shown. All wavelengths are given

Which diagram shows the corresponding part of the absorption spectrum observed from Earth emitted from a galaxy moving away with a velocity of 0.031 c?

Your answer

An astronomer analyses the light from a distant galaxy. One of the spectral lines in the spectrum observed from the galaxy has wavelength 610 nm. The same spectral line has a wavelength of 590 nm when measured in the laboratory.

What is the speed of this galaxy?

9.8 × 10⁶ m s^–1 A

1.0 × 10⁷ m s^–1 B

2.9 × 10⁸ m s^–1 C

3.0 × 10⁸ m s^–1 D

Your answer

Describe the Doppler effect.

Explain how ultrasound is used to measure the speed of blood flow in an artery.

Use Fig. 6.2 to show that the speed of the loudspeaker is 7.5 m s^–1. (i)

The speed of sound in this experiment is 330 m s^–1. (ii)

Calculate the maximum change in frequency f of the sound detected by the microphone.

Hence complete the scale on the y-axis of Fig. 6.2.

Mark with an X on Fig. 6.1 the position of the loudspeaker which corresponds to the

point X on Fig. 6.2.

In their laboratory notes, one student writes about the accuracy of the measurements whereas the other writes about their precision.

Define these terms.

A binary star is a pair of stars which move in circular orbits around their common centre of mass.

In this question consider the stars to be point masses situated at their centres.

Fig. 3.1 shows a binary star where the mass of each star is m. The stars move in the same circular orbit.

Explain why the stars of equal mass must always be diametrically opposite as they travel in the circular orbit.

The stars are viewed from Earth in the plane of rotation. The stars are observed using light that has wavelength of 656 nm in the laboratory. The observed light from the stars is Doppler shifted.

Calculate the maximum change in the observed wavelength of this light from the orbiting stars. Give your answer in nm.

The centre of mass of the binary star lies at the surface of the star of mass 4 m. Draw on

Fig. 3.2 two circles to represent the orbits of both stars.

Explain why the smaller mass star travels faster in its orbit than the larger mass star.

Part of the line spectrum for light from the Sun is shown below.

Which spectrum best shows light from a similar star to the Sun?

Your answer

Explain why the energy levels are negative.

An electron makes a transition (jump) from level C to level A.

1 Calculate the energy gained by this electron.

2 Calculate the wavelength in nm of the photon absorbed by this electron.

State how an emission line is produced.

State an adjustment that could be made to the experimental arrangement that would space the emission lines more widely.

In the laboratory, the wavelength of the hydrogen-alpha emission line is 656.3 nm. Use Fig. 21.2 to determine the recession velocity of the galaxy.

recession velocity =........ m s⁻¹

Suggest why hydrogen spectral lines play an important role in determining red shift of galaxies.

Light from a similar star is viewed in a galaxy further away. The star is part of a pair of stars which orbit a common centre of mass. Describe and explain how the equivalent spectrum might appear.