CAIE A-Level Physics A2 25 Astronomy and Cosmology Questions

Practise using stellar and galaxy evidence for distances, temperatures, radii, redshift, Hubble’s law, cosmic expansion and the Big Bang.

Exam points

use luminosity, radiant flux and standard-candle observations to determine stellar or galaxy distances
apply Wien?s displacement law and Stefan?Boltzmann law to infer stellar temperature, luminosity and radius
identify and calculate redshift from spectral data
use redshift relationships to determine recession speed or wavelength/frequency change
explain the evidence for an expanding Universe
use Hubble?s law to estimate distance and connect cosmic expansion to the Big Bang

Covered syllabus points

25.1 Standard candles 25.2 Stellar radii 25.3 Hubble’s law and the Big Bang theory

[Maximum number: 9]

(a)

State what is meant by the luminosity of a star.

[ 2 ]

(b)

Explain how a standard candle in a distant galaxy can be used to determine the distance of the galaxy from an observer.

[ 3 ]

standard candle has known luminosity
radiant flux intensity measured by observer
(distance calculated using) $F=L / 4 \pi d^{2}$

(c)

The Sun has a radius of $6.96 \times 10^{8} \mathrm{~m}$ and a surface temperature of 5780 K . Light from the Sun is observed to have a peak intensity at a wavelength of 501 nm .

[ 4 ]

(i)

Calculate the luminosity of the Sun. Give a unit with your answer.

luminosity =

unit

[ 2 ]

luminosity $=4 \pi \sigma r^{2} T^{4}$ $=4 \pi \times 5.67 \times 10^{-8} \times\left(6.96 \times 10^{8}\right)^{2} \times 5780^{4}$ $=3.85 \times 10^{26} \mathrm{~W}$

(ii)

Another star emits radiation that has a peak intensity at a wavelength of 624 nm .

Determine the surface temperature of this star.
surface temperature =

[ 2 ]

$\lambda_{\text {max }} T=$ constant
temperature $=(5780 \times 501) / 624$ $\text { = } 4640 \mathrm{~K}$

[Maximum number: 8]

(a)

State what is meant by the luminosity of a star.

[ 1 ]

(b)

A star in the constellation Canis Major is a distance of $8.14 \times 10^{16} \mathrm{~m}$ from the Earth and has a luminosity of $9.86 \times 10^{27} \mathrm{~W}$ . The surface temperature of the star is 9830 K .

[ 4 ]

(i)

Calculate the radiant flux intensity of the radiation from the star observed from the Earth. Give a unit with your answer.
radiant flux intensity = unit

[ 2 ]

$F=L /\left(4 \pi d^{2}\right)$ $\begin{aligned} =9.86 \times 10^{27} /\left[4 \pi \times\left(8.14 \times 10^{16}\right)^{2}\right] =1.18 \times 10^{-7} \mathrm{Wm}^{-2} \end{aligned}$

(ii)

Determine the radius of the star.
radius = m

[ 2 ]

$\begin{aligned} L=4 \pi \sigma r^{2} T^{4} 9.86 \times 10^{27}=4 \times \pi \times 5.67 \times 10^{-8} \times r^{2} \times 9830^{4} \end{aligned}$
radius $=1.22 \times 10^{9} \mathrm{~m}$

(c)

Explain how the surface temperature of a distant star may be determined from the wavelength spectrum of the light from the star.

[ 3 ]

[Maximum number: 9]

(a)

State Wien's displacement law.

[ 1 ]

(b)

Fig. 10.1 shows the wavelength distributions of electromagnetic radiation emitted by two stars A and B .

Fig. 10.1

The surface temperature of star A is known to be 5800 K .

[ 4 ]

(i)

Determine the surface temperature of star B .
surface temperature = K

[ 2 ]

$\lambda_{\text {MAX }}=0.50 \mu \mathrm{~m}$ for A and $0.65 \mu \mathrm{~m}$ for B
$\begin{aligned} T =5800 \times(0.50 / 0.65) =4500 \mathrm{~K} \end{aligned}$

(ii)

Star B appears less bright than star A when viewed from the Earth.

Use Fig. 10.1 to suggest, with a reason, how else the physical appearance of star B compares with that of star A.

[ 2 ]

(c)

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: 9]

(a)

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

[ 2 ]

(b)

A star of luminosity $3.8 \times 10^{31} \mathrm{~W}$ is a distance of $1.8 \times 10^{24} \mathrm{~m}$ from the Earth.

Calculate the radiant flux intensity at the Earth of the radiation emitted by the star.
radiant flux intensity = $\mathrm{Wm}^{-2}$

[ 2 ]

$F=L /\left(4 \pi d^{2}\right)$ $\begin{aligned} =\left(3.8 \times 10^{31}\right) /\left[4 \pi \times\left(1.8 \times 10^{24}\right)^{2}\right] =9.3 \times 10^{-19} \mathrm{~W} \mathrm{~m}^{-2} \end{aligned}$

(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 .

[ 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}=

$\mathrm{s}^{-1}$

[ 3 ]

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

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