CAIE A-Level Physics 25 Astronomy and Cosmology

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

Covered syllabus points

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

[Maximum number: 6]

(a)

State what is meant by luminosity of a star.

[ 1 ]

(b)

The luminosity of the Sun is $3.83 \times 10^{26} \mathrm{~W}$ . The distance between the Earth and the Sun is $1.51 \times 10^{11} \mathrm{~m}$ .

Calculate the radiant flux intensity F of the Sun at the Earth. Give a unit with your answer.

unit

[ 2 ]

$\begin{aligned} F=\frac{L}{4 \pi d^{2}} =\frac{3.83 \times 10^{26}}{4 \times \pi \times 1.51 \times 10^{112}} \end{aligned}$

C1

$=1340 \mathrm{~W} \mathrm{~m}^{-2}$

A1

(c)

The radius of the Sun is $6.96 \times 10^{8} \mathrm{~m}$ .

Show that the temperature T of the surface of the Sun is 5770 K .

[ 1 ]

$\begin{aligned} \mathrm{L}=4 \pi \sigma r^{2} \mathrm{~T}^{4} 3.83 \times 10^{26}=4 \times \pi \times 5.67 \times 10^{-8} \times 6.96 \times 10^{82} \times \mathrm{T}^{4} \text { leading to } \mathrm{T}=5770 \mathrm{~K} \end{aligned}$

B1

(d)

The wavelength $\lambda_{\text {max }}$ of light for which the maximum rate of emission occurs from the Sun is $5.00 \times 10^{-7} \mathrm{~m}$ .
The temperature of the surface of the star Sirius is 9940 K .
Use information from (d) to determine the wavelength of light for which the maximum rate of emission occurs from Sirius.
wavelength =
m

[ 2 ]

$\begin{aligned} \lambda_{(\max )} \propto \frac{1}{\mathrm{~T}} \frac{5.00 \times 10^{-7}}{\lambda}=\frac{9940}{5770} \end{aligned}$

C1

$\lambda=2.90 \times 10^{-7} \mathrm{~m}$

A1

[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

C1

$\begin{aligned} T =5800 \times(0.50 / 0.65) =4500 \mathrm{~K} \end{aligned}$

A1

(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 ]

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Covered syllabus points

25. Astronomy and cosmology question 1

Question (a)

Question (b)

Question (c)

Question (d)

25. Astronomy and cosmology question 2

Question (a)

Question (b)

Question (i)

Question (ii)

Question (c)

Question (i)

Question (ii)