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A-Level CAIE Physics 25 3 Hubble S Law And The Big Bang Theory Question Bank

Practice A-Level CAIE Physics 25 3 Hubble S Law And The Big Bang Theory questions by syllabus topic with past-paper context, marks, difficulty and question previews on Eduninja.

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Question 8

8

Fig． 8.1 shows part of the emission spectrum of visible radiation emitted by hydrogen gas in a star in a distant galaxy． The galaxy is moving away from the Earth at a speed of \(6.2 \times 10^{6} \mathrm{~ms}^{-1}\) ．

structured8 marks

Question 8(a)

8(a)

4 marks

Question 8(a)(i)

8(a)(i)

（a）（i）Explain how the positions of the lines in the emission spectrum seen by an observer on the Earth differ from the positions shown in Fig．8．1．

Mediumstructured2 marks

Answer

movement of star causes change in (observed) frequency or movement of star causes redshift B1 observed frequency is lower (than emitted frequency) B1

Question 8(a)(ii)

8(a)(ii)

（ii）On Fig．8．1，draw the three lines in possible positions in the spectrum seen by the observer． （b）The lines in Fig． 8.1 correspond to electron transitions down to the energy level -3.40 eV ． One of the lines represents emitted radiation of wavelength 488 nm ．

Mediumstructured2 marks

Answer

all three lines shown to left of corresponding printed lines B1 distance between drawn line and corresponding printed line approximately the same for all three lines B1

Question 8(b)

8(b)

2 marks

Question 8(b)(iii)

8(b)(iii)

Determine the wavelength, in nm , of this radiation as detected by the observer on the Earth. wavelength = nm

Mediumstructured2 marks

Answer

\[ \begin{aligned} \Delta \lambda =\lambda \times(v / c) =\left(488 \times 6.2 \times 10^{6}\right) /\left(3.00 \times 10^{8}\right) =10 \mathrm{~nm}) \end{aligned} \] C1 \[ \begin{aligned} \text { observed wavelength } =488+\Delta \lambda=488+10 =498 \mathrm{~nm} \end{aligned} \] A1

Question 8(c)

8(c)

A value for the Hubble constant is \(2.3 \times 10^{-18} \mathrm{~s}^{-1}\). Determine the distance of the galaxy from the Earth. distance = m

Mediumstructured2 marks

Answer

\(v \quad=H_{0} d\) C1 \[ \begin{aligned} d =\left(6.2 \times 10^{6}\right) /\left(2.3 \times 10^{-18}\right) =2.7 \times 10^{24} \mathrm{~m} \end{aligned} \] A1

Question 9

9

7 marks

Question 9(b)

9(b)

The same part of the emission spectrum from hydrogen as in (a), observed in light from stars in a distant galaxy, is shown in Fig. 9.3. The numbers indicate the wavelengths in nm . The spectrum shows the same pattern as Fig. 9.1 but with different wavelengths.

structured5 marks

Question 9(b)(i)

9(b)(i)

State the name of the phenomenon that gives rise to the change in the wavelengths.

Easystructured1 marks

Answer

redshift B1

Question 9(b)(ii)

9(b)(ii)

State what this phenomenon shows about the motion of the galaxy.

Mediumstructured1 marks

Answer

moving away (from observer) B1

Question 9(b)(iii)

9(b)(iii)

Use one of the lines in Fig. 9.1, and the corresponding line in Fig. 9.3, to determine the speed of the distant galaxy relative to the observer. speed = \(\mathrm{m} \mathrm{s}^{-1}\)

Hardstructured3 marks

Answer

\[ \Delta \lambda / \lambda=v / c \] e.g. for 658 nm line: \(\Delta \lambda=686-658\) \[ \text { ( = } 28 \text { nm) (other lines may be used) } \] C1 \(28 / 658=v /\left(3.00 \times 10^{8}\right)\) (other lines may be used) C1 \(v=1.3 \times 10^{7} \mathrm{~m} \mathrm{~s}^{-1}\) A1

Question 9(c)

9(c)

The galaxy in (b) is known to be a distance of \(5.7 \times 10^{24} \mathrm{~m}\) from the Earth. Use your answer in (b)(iii) to determine a value for the Hubble constant \(H_{0}\).

Hardstructured2 marks

Answer

\(v=H_{0} d\) C1 \[ \begin{aligned} H_{0} =\left(1.3 \times 10^{7}\right) /\left(5.7 \times 10^{24}\right) =2.3 \times 10^{-18} \mathrm{~s}^{-1} \end{aligned} \] A1

Question 9

9

7 marks

Question 9(a)

9(a)

4 marks

Question 9(a)(i)

9(a)(i)

State Hubble's law.

Easystructured2 marks

Answer

speed is (directly) proportional to distance M1 where speed is speed of recession of galaxy (from observer) and distance is distance of galaxy away from observer A1

Question 9(a)(ii)

9(a)(ii)

Explain how cosmologists use observations of emission spectra from stars in distant galaxies to determine that the Universe is expanding.

Mediumstructured2 marks

Answer

wavelengths (of spectral lines) are greater (than their known values) B1 redshift shows stars (in distant galaxies) moving away from Earth B1

Question 9(b)

9(b)

Explain how Hubble's law and the idea of the expanding Universe lead to the Big Bang theory of the origin of the Universe.

Hardstructured3 marks

Answer

(all) parts of Universe moving away from each other B1 more distant objects are moving away faster B1 matter must have been close together / very dense in the past B1

Question 10

10

6 marks

Question 10(c)

10(c)

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 .

structured6 marks

Question 10(c)(i)

10(c)(i)

Show that the speed of the star relative to the Earth is \(2.1 \times 10^{6} \mathrm{~ms}^{-1}\).

Mediumstructured1 marks

Answer

\(\frac{660.9-656.3}{656.3} \approx \frac{v}{3.0 \times 10^{8}}\) leading to \(2.1 \times 10^{6} \mathrm{~m} \mathrm{~s}^{-1}\) B1

Question 10(c)(ii)

10(c)(ii)

Calculate the distance to the star. The Hubble constant is \(2.3 \times 10^{-18} \mathrm{~s}^{-1}\). distance = m

Mediumstructured2 marks

Answer

\(v=H_{0} d\) C1 \[ \begin{aligned} d =2.1 \times 10^{6} / 2.3 \times 10^{-18} =9.1 \times 1023 \mathrm{~m} \end{aligned} \] A1

Question 10(c)(iii)

10(c)(iii)

State and explain what can be concluded about the Universe based on this change in observed wavelength.

Mediumstructured3 marks

Answer

wavelength has increased / light is redshifted B1 star within galaxy is moving away / receding (from Earth) B1 Universe is expanding B1

Question 10

10

4 marks

Question 10(b)

10(b)

A galaxy in the constellation Corona Borealis is moving away from the Earth.

structured4 marks

Question 10(b)(i)

10(b)(i)

The visible emission spectrum for the Sun is shown in Fig. 10.2. The lines are at wavelengths of \(397 \mathrm{~nm}, 410 \mathrm{~nm}, 434 \mathrm{~nm}, 486 \mathrm{~nm}\) and 656 nm . The compositions of the Sun and a star in the Corona Borealis galaxy are similar. On Fig. 10.3, sketch the emission spectrum for the star in the Corona Borealis galaxy as observed from the Earth. No calculations are required.

Mediumstructured1 marks

Answer

5 lines in same pattern shifted to longer wavelengths B1

Question 10(b)(ii)

10(b)(ii)

The galaxy in Corona Borealis is moving away from the Earth at a speed of \(21400 \mathrm{~km} \mathrm{~s}^{-1}\). Use information from (b)(i) to calculate, in nm , the observed wavelength of the lowest visible energy emission for the star in the Corona Borealis galaxy. wavelength = nm

Mediumstructured2 marks

Answer

\[ \begin{aligned} \Delta \lambda / \lambda=v / c \Delta \lambda=(21400 / 300000) \times 656 =46.8 \mathrm{~nm} \end{aligned} \] C1 \[ \begin{aligned} \text { wavelength } =656+46.8 =703 \mathrm{~nm} \end{aligned} \] A1

Question 10(b)(iii)

10(b)(iii)

The wavelength in (b)(ii) is used to calculate a value for the surface temperature of the star in the Corona Borealis galaxy. The calculation does not give an accurate value. State and explain whether this value of temperature is too high or too low.

Hardstructured1 marks

Answer

(peak) wavelength too high so temperature too low B1

Question 10

10

4 marks

Question 10(c)

10(c)

The lines in Fig. 10.1 have been corrected for redshift.

structured4 marks

Question 10(c)(i)

10(c)(i)

State what is meant by redshift.

Easystructured2 marks

Answer

apparent wavelength is greater or wavelength is greater than known value B1 (due to) movement of star away (from observer) B1

Question 10(c)(ii)

10(c)(ii)

Explain how cosmologists are able to determine that light from a distant star has undergone redshift.

Mediumstructured2 marks

Answer

by examining the (lines in the) spectrum (of light from the star) B1 and comparing with known spectrum B1

Question 10

10

5 marks

Question 10(b)

10(b)

A cosmology student observes the electromagnetic radiation received from a star in a galaxy. The student uses Wien's law to estimate the surface temperature of the star, a standard candle to estimate the distance to the galaxy, and the Stefan-Boltzmann law to estimate the radius of the star. The student observes that the radiation from the star is redshifted.

structured5 marks

Question 10(b)(ii)

10(b)(ii)

State the reason why the radiation from the star is redshifted.

Mediumstructured1 marks

Answer

star / galaxy is moving away from the student B1

Question 10(b)(iii)

10(b)(iii)

The true values of the quantities observed or estimated are those that are corrected to allow for redshift. However, the student does not correct for redshift. By placing one tick \((\checkmark)\) in each row, complete Table 10.1 to indicate how the observations and estimates made by the student compare with the true values.

Hardstructured4 marks

Answer

one tick placed in correct column in each row: wavelength: too high B1 surface temperature: too low B1 distance: unchanged B1 radius: too high B1

Question 10

10

7 marks

Question 10(a)

10(a)

State Hubble's law. Identify any symbols that you use.

Easystructured2 marks

Answer

speed is (directly) proportional to distance M1 speed is speed of recession of galaxy from an observer, and distance is the distance of the galaxy from the observer A1

Question 10(c)

10(c)

The star in (b) 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 .

structured5 marks

Question 10(c)(i)

10(c)(i)

Explain why the wavelength observed on the Earth is different from the wavelength that the galaxy is known to have emitted.

Mediumstructured2 marks

Answer

galaxy is moving away (from the Earth) B1 wavelength (of light from the galaxy) increased by the Doppler effect / due to redshift B1

Question 10(c)(ii)

10(c)(ii)

Determine a value for the Hubble constant \(H_{0}\).

Hardstructured3 marks

Answer

\[ \begin{aligned} \Delta \lambda / \lambda=v / c v=\left[(492-486) \times 3.00 \times 10^{8}\right] / 486 \left(v=3.7 \times 10^{6} \mathrm{~m} \mathrm{~s}^{-1}\right) \end{aligned} \] C1 \(H_{0}=v / d\) C1 \[ \begin{aligned} =\left(3.7 \times 10^{6}\right) /\left(1.8 \times 10^{24}\right) =2.1 \times 10^{-18} \mathrm{~s}^{-1} \end{aligned} \] A1

Question 10

10

7 marks

Question 10(a)

10(a)

State Hubble's law. Identify any symbols that you use.

Easystructured2 marks

Answer

speed is (directly) proportional to distance M1 speed is speed of recession of galaxy from an observer, and distance is the distance of the galaxy from the observer A1

Question 10(c)

10(c)

The star in (b) 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 .

structured5 marks

Question 10(c)(i)

10(c)(i)

Explain why the wavelength observed on the Earth is different from the wavelength that the galaxy is known to have emitted.

Mediumstructured2 marks

Answer

galaxy is moving away (from the Earth) B1 wavelength (of light from the galaxy) increased by the Doppler effect / due to redshift B1

Question 10(c)(ii)

10(c)(ii)

Determine a value for the Hubble constant \(H_{0}\). \(\mathrm{s}^{-1}\)

Hardstructured3 marks

Answer

\[ \begin{aligned} \Delta \lambda / \lambda=v / c v=\left[(492-486) \times 3.00 \times 10^{8}\right] / 486 \left(v=3.7 \times 10^{6} \mathrm{~m} \mathrm{~s}^{-1}\right) \end{aligned} \] C1 \(H_{0}=v / d\) C1 \[ \begin{aligned} =\left(3.7 \times 10^{6}\right) /\left(1.8 \times 10^{24}\right) =2.1 \times 10^{-18} \mathrm{~s}^{-1} \end{aligned} \] A1

Question 12

12

2 marks

Question 12(a)

12(a)

State two reasons why frequencies in the gigahertz (GHz) range are used in satellite communication. 1. 2.

Mediumstructured2 marks

Answer

e.g. no/little ionospheric reflection large information carrying capacity (any two sensible suggestions, 1 each) B2 [2]