1. 1
   The Sun is a main-sequence star that has been stable for about 4.6 billion years. In its core, where the temperature is about 1.5 × 10⁷ K and the density is about 1.5 × 10⁵ kg m⁻³, hydrogen nuclei fuse to form helium. Energy released in the core travels outwards and is eventually radiated from the surface.

   (a)

   Which two effects must be in equilibrium for the Sun to remain a stable size?

   [1 mark]

   • AOutward strong nuclear force and inward gravitational force
   • BOutward gravitational force and inward radiation pressure
   • COutward magnetic force and inward electrostatic force
   • DOutward radiation pressure and inward gravitational force

   (b)

   Why do fusion reactions in the core need both a high temperature and a high density?

   [1 mark]

   • AHigh temperature makes the strong force repulsive, and high density pushes nuclei together against it
   • BHigh temperature gives nuclei enough kinetic energy to overcome their electrostatic repulsion, and high density makes collisions frequent enough
   • CHigh temperature splits helium into hydrogen, and high density stops the hydrogen escaping
   • DHigh temperature increases the mass of each proton, and high density increases the binding energy of hydrogen

   (c)

   Explain why the fusion of hydrogen into helium releases energy.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   An astronomer records the luminosity, in terms of the Sun's luminosity L☉, and the surface temperature of four stars. Star W: 1.0 × 10⁻² L☉ and 9000 K. Star X: 1.0 L☉ and 5800 K. Star Y: 1.0 × 10⁴ L☉ and 3500 K. Star Z: 3.0 × 10⁴ L☉ and 30 000 K.

   (a)

   Which star is a white dwarf?

   [1 mark]

   • AW
   • BX
   • CY
   • DZ

   (b)

   Which star has the largest radius?

   [1 mark]

   • AW
   • BX
   • CY
   • DZ

   (c)

   Determine the ratio radius of Z ÷ radius of X.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   An astronomer measures the stellar parallax angle of a nearby star as 0.025 arc-second. The apparent brightness of the star, measured at Earth, is 4.2 × 10⁻¹⁰ W m⁻². The peak wavelength in the star's spectrum is 290 nm. One parsec is 3.09 × 10¹⁶ m and the radius of the Sun is 6.96 × 10⁸ m.

   (a)

   Determine the luminosity of the star.

   [3 marks]

   (b)

   Determine the radius of the star in terms of the Sun's radius, and deduce the region of the Hertzsprung–Russell diagram in which the star lies.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Two stars, P and Q, formed at the same time in the same star cluster. Star P has the mass of the Sun (1 M☉) and a luminosity of 1 L☉. Star Q has a mass of 15 M☉ and a luminosity of about 1.3 × 10⁴ L☉. Both are currently fusing hydrogen in their cores. The main-sequence lifetime of a star like P is about 1 × 10¹⁰ years.

   (a)

   Explain how a star remains stable on the main sequence and why the core of Q can fuse elements much heavier than those fused in the core of P.

   [6 marks]

   (b)

   Using the data, discuss how the difference in mass between P and Q affects their main-sequence lifetimes and their final stages of evolution.

   [6 marks]

   Total for question 4: 12 marks

End of questions