CAIE A-Level Physics A2 25.3 Hubbles Law and the Big Bang Theory Questions

Practise quantifying redshift, calculating recession speed with spectral data, applying Hubble’s law and linking expansion evidence to the Big Bang.

Exam points

identify and quantify redshift by comparing observed and known spectral lines
use ??/? ? ?f/f ? v/c to determine recession speed or spectral shift
explain how redshift observations support an expanding Universe
use Hubble?s law to calculate cosmic distance or recession speed and relate it to the Big Bang

Covered syllabus points

25.3.1—The lines in the emission and absorption spectra 25.3.2—Redshift of electromagnetic radiation 25.3.3—Why redshift leads to the idea that the universe is expanding 25.3.4—Hubble’s law v ≈ H0d and explain how this leads to the Big Bang theory

[Maximum number: 4]

(a)

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

[ 4 ]

(i)

State what is meant by redshift.

[ 2 ]

(ii)

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

[ 2 ]

[Maximum number: 7]

(a)

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

[ 2 ]

(b)

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 .

[ 5 ]

(i)

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

[ 2 ]

(ii)

Determine a value for the Hubble constant $H_{0}$ .

H_{0}=\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . . s^{-1}

[ 3 ]

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

[Maximum number: 6]

(a)

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 .

[ 6 ]

(i)

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

[ 1 ]

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

(ii)

Calculate the distance to the star.

The Hubble constant is $2.3 \times 10^{-18} \mathrm{~s}^{-1}$ .
distance = m

[ 2 ]

$v=H_{0} d$ $\begin{aligned} d =2.1 \times 10^{6} / 2.3 \times 10^{-18} =9.1 \times 1023 \mathrm{~m} \end{aligned}$

(iii)

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

[ 3 ]

[Maximum number: 2]

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

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

[Maximum number: 2]

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

[Maximum number: 3]

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 .

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

[Maximum number: 2]

Fig． 8.1 shows part of the emission spectrum of visible radiation emitted by hydrogen gas in a star in a distant galaxy．

Fig． 8.1

The galaxy is moving away from the Earth at a speed of $6.2 \times 10^{6} \mathrm{~ms}^{-1}$ ．

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

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

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Covered syllabus points

Question 1

Question (a)

Question (i)

Question (ii)

Question 2

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Question (b)

Question (i)

Question (ii)

Question 3

Question (a)

Question (i)

Question (ii)

Question (iii)

Question 4

Question 5

Question 6

Question 7