25.3. Hubble’s law and the Big Bang theory
A subsection of Physics, 9702, through 25. Astronomy and cosmology
Listing 8 of 8 questions
A student observes different stars from the Earth. Give two reasons why some stars appear brighter than others. State what is meant by a standard candle. A spectral line from a star within a galaxy is observed to have a wavelength of 660.9 nm. The same spectral line measured in the laboratory is observed to have a wavelength of 656.3 nm. Show that the speed of the star relative to the Earth is 2.1 × 106 m s–1. Calculate the distance to the star. The Hubble constant is 2.3 × 10–18 s–1. distance = m State and explain what can be concluded about the Universe based on this change in observed wavelength.
9702_m23_qp_42
THEORY
2023
Paper 4, Variant 2
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State Hubble’s law. Identify any symbols that you use. A star of luminosity 3.8 × 1031 W is a distance of 1.8 × 1024 m from the Earth. Calculate the radiant flux intensity at the Earth of the radiation emitted by the star. radiant flux intensity = W m–2 The star in is in a distant galaxy. A spectral line in the light from this galaxy is known to have a wavelength of 486 nm. This spectral line in the light from the galaxy observed on the Earth has a wavelength of 492 nm. Explain why the wavelength observed on the Earth is different from the wavelength that the galaxy is known to have emitted. Determine a value for the Hubble constant H0. H0 = s–1
9702_s23_qp_41
THEORY
2023
Paper 4, Variant 1
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State Hubble’s law. Identify any symbols that you use. A star of luminosity 3.8 × 1031 W is a distance of 1.8 × 1024 m from the Earth. Calculate the radiant flux intensity at the Earth of the radiation emitted by the star. radiant flux intensity = W m–2 The star in is in a distant galaxy. A spectral line in the light from this galaxy is known to have a wavelength of 486 nm. This spectral line in the light from the galaxy observed on the Earth has a wavelength of 492 nm. Explain why the wavelength observed on the Earth is different from the wavelength that the galaxy is known to have emitted. Determine a value for the Hubble constant H0. H0 = s–1
9702_s23_qp_43
THEORY
2023
Paper 4, Variant 3
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shows part of the emission spectrum of visible radiation emitted by hydrogen gas in a star in a distant galaxy. increasing frequency The galaxy is moving away from the Earth at a speed of 6.2 × 106 m s–1. Explain how the positions of the lines in the emission spectrum seen by an observer on the Earth differ from the positions shown in . On , draw the three lines in possible positions in the spectrum seen by the observer. The lines in correspond to electron transitions down to the energy level –3.40 eV. One of the lines represents emitted radiation of wavelength 488 nm. Calculate the energy of a photon of this radiation. photon energy = J Determine the energy, in eV, of the energy level from which the electron transition originates to cause the emission of this radiation. energy level = eV Determine the wavelength, in nm, of this radiation as detected by the observer on the Earth. wavelength = nm A value for the Hubble constant is 2.3 × 10–18 s–1. Determine the distance of the galaxy from the Earth. distance = m ,  ,
9702_s24_qp_42
THEORY
2024
Paper 4, Variant 2
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shows the visible part of the emission spectrum from hydrogen gas in a laboratory on the Earth. The numbers indicate the wavelength, in nm, represented by each line. Explain how the emission spectrum provides evidence for the existence of discrete energy levels for the electron in a hydrogen atom. shows five of the energy levels in the hydrogen atom. The wavelengths of radiation shown in relate to transitions to the – 3.400 eV level in . energy – 0.378 eV – 0.544 eV – 0.850 eV X – 3.400 eV (not to scale) Show that the energy level X is –1.51 eV. The same part of the emission spectrum from hydrogen as in , observed in light from stars in a distant galaxy, is shown in . The numbers indicate the wavelengths in nm. The spectrum shows the same pattern as but with different wavelengths. State the name of the phenomenon that gives rise to the change in the wavelengths. State what this phenomenon shows about the motion of the galaxy. Use one of the lines in , and the corresponding line in , to determine the speed of the distant galaxy relative to the observer. speed = m s–1 The galaxy in is known to be a distance of 5.7 × 1024 m from the Earth. Use your answer in to determine a value for the Hubble constant H0. H0 = s–1
9702_w22_qp_42
THEORY
2022
Paper 4, Variant 2
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Explain how redshift leads to the idea that the Universe is expanding. Stars in a distant galaxy emit radiation. The total luminosity of the stars in the galaxy is 1.90 × 1036 W. The emission spectrum of the radiation contains a line X at a wavelength of 658 nm. Radiation from the galaxy is observed on the Earth. The observed radiation has a radiant flux intensity of 8.42 × 10–16 W m–2. In the observed emission spectrum, line X is at a wavelength of 726 nm. Determine: the distance d of the galaxy from the Earth d = m the speed v of the galaxy relative to the Earth. v = m s–1 Observations of many galaxies, such as the one in , lead to many pairs of values of d and v. Plotting these values reveals a trend. On , sketch the variation of v with d. d v State the name of the quantity represented by the gradient of the line in .
9702_w24_qp_41
THEORY
2024
Paper 4, Variant 1
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Explain how redshift leads to the idea that the Universe is expanding. Stars in a distant galaxy emit radiation. The total luminosity of the stars in the galaxy is 1.90 × 1036 W. The emission spectrum of the radiation contains a line X at a wavelength of 658 nm. Radiation from the galaxy is observed on the Earth. The observed radiation has a radiant flux intensity of 8.42 × 10–16 W m–2. In the observed emission spectrum, line X is at a wavelength of 726 nm. Determine: the distance d of the galaxy from the Earth d = m the speed v of the galaxy relative to the Earth. v = m s–1 Observations of many galaxies, such as the one in , lead to many pairs of values of d and v. Plotting these values reveals a trend. On , sketch the variation of v with d. d v State the name of the quantity represented by the gradient of the line in .
9702_w24_qp_43
THEORY
2024
Paper 4, Variant 3
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Questions Discovered
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