Black-body radiation and stellar luminosityEdexcel International A Level Physics: Subtopic test

1. 1
   A star of radius 6.96 × 10⁸ m has a surface temperature of 5.80 × 10³ K and may be treated as a black body radiator. A planet orbits it at a distance of 1.50 × 10¹¹ m. Use: Stefan–Boltzmann constant σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴; Wien's law constant = 2.898 × 10⁻³ m K.

   (a)

   What is the wavelength at which the star radiates with maximum intensity?

   [1 mark]

   • A2.0 × 10⁶ m
   • B5.0 × 10⁻⁷ m
   • C1.7 × 10¹ m
   • D5.0 × 10⁻⁴ m

   (b)

   What is the luminosity of the star?

   [1 mark]

   • A3.1 × 10²⁵ W
   • B9.8 × 10²⁵ W
   • C3.9 × 10²⁶ W
   • D2.0 × 10¹⁵ W

   (c)

   Calculate the intensity of the radiation from the star at the planet.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Two stars, A and B, have the same radius and may both be treated as black body radiators. The surface temperature of star A is 3500 K and that of star B is 7000 K. Use: Stefan–Boltzmann constant σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴; Wien's law constant = 2.898 × 10⁻³ m K.

   (a)

   How does the wavelength of maximum intensity of star B compare with that of star A?

   [1 mark]

   • AIt is half as long
   • BIt is twice as long
   • CIt is the same
   • DIt is one quarter as long

   (b)

   What is the ratio of the luminosity of star B to the luminosity of star A?

   [1 mark]

   • A2
   • B4
   • C8
   • D16

   (c)

   Explain why star B appears bluer than star A.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   An astronomer studies a star that radiates as a black body with a luminosity of 2.5 × 10²⁸ W. The star is at a distance of 8.1 × 10¹⁶ m from the Earth. The wavelength at which the radiation from the star has maximum intensity is 293 nm. Use: Stefan–Boltzmann constant σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴; Wien's law constant = 2.898 × 10⁻³ m K.

   (a)

   Calculate the intensity of the radiation from the star at the Earth.

   [3 marks]

   (b)

   Determine the radius of the star.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Astronomers model stars as black body radiators. A red supergiant star has a surface temperature of 3500 K and a radius of 5.5 × 10¹¹ m. The Sun has a surface temperature of 5800 K, a radius of 6.96 × 10⁸ m and a luminosity of 3.9 × 10²⁶ W. Use: Stefan–Boltzmann constant σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴; Wien's law constant = 2.898 × 10⁻³ m K.

   (a)

   Describe how the spectrum of radiation from a black body radiator changes as its temperature increases, and explain how this affects the colour of a star.

   [6 marks]

   (b)

   Calculate the luminosity of the red supergiant and compare it with the luminosity of the Sun. Explain how a star cooler than the Sun can be so much more luminous.

   [6 marks]

   Total for question 4: 12 marks

End of questions