OCR A Physics · Module 5: Newtonian world and astrophysics
Astrophysics & cosmology: practice questions with answers
6 exam-style questions on astrophysics & cosmology. Try each one on paper first, then open the answer to see the full working and the common slips that cost marks.
- Standard form3 marks
A star has radius 1.74 × 10⁹ m and surface temperature 5800 K. Treating it as a black body, calculate its luminosity.
L = W
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Answer L = 2.44 × 10²⁷ W
L = 4πr²σT⁴ = 4π × (1.74 × 10⁹)² × 5.67 × 10⁻⁸ × 5800⁴ = 2.44 × 10²⁷ W.
- Got 6.10 × 10²⁶ W? You left out the factor of 4. The surface area is 4πr², so L = 4πr²σT⁴ = 2.44 × 10²⁷ W.
- Got 1.40 × 10¹⁸ W? You did not square the radius. L = 4πr²σT⁴ = 2.44 × 10²⁷ W.
- Unit prefixes2 marks
The peak wavelength of light from a star is 420 nm. Use Wien's law, λmax T = 2.90 × 10⁻³ m K, to calculate its surface temperature.
T = K
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Answer T = 6910 K
T = 2.90 × 10⁻³ ÷ λmax = 2.90 × 10⁻³ ÷ 4.20 × 10⁻⁷ = 6.9e+03 K.
- Got 6.90 × 10⁻⁶ K? You used 420 m. λmax = 420 × 10⁻⁹ m, so T = 2.90 × 10⁻³ ÷ 4.20 × 10⁻⁷ = 6.9e+03 K.
- Got 1.22 × 10⁻⁹ K? You multiplied instead of dividing. T = (2.90 × 10⁻³) ÷ λmax = 6.9e+03 K.
- Unit prefixes3 marks
The Hubble constant is 70 km s⁻¹ Mpc⁻¹. Use 1 Mpc = 3.09 × 10²² m and 1 year = 3.16 × 10⁷ s to estimate the age of the universe, 1/H₀, in billions of years.
t = billion years
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Answer t = 14 billion years
H₀ = 70 × 10³ ÷ 3.09 × 10²² = 2.27 × 10⁻¹⁸ s⁻¹. 1/H₀ = 4.41 × 10¹⁷ s, which is 14 billion years.
- Got 14000 billion years? You did not convert km to m, so H₀ was wrong by 1000. H₀ = 70 × 10³ ÷ 3.09 × 10²² = 2.27 × 10⁻¹⁸ s⁻¹ and t = 1 ÷ H₀ = 14 billion years.
- Got 4.41 × 10⁸ billion years? You have not converted seconds to years. 1/H₀ = 4.41 × 10¹⁷ s, and dividing by 3.16 × 10⁷ s per year gives 14 billion years.
- Using the right equation2 marks
A hydrogen line of rest wavelength 656.3 nm is observed in a galaxy's spectrum at 662.0 nm. Calculate the recession speed of the galaxy, in km s⁻¹.
v = km s⁻¹
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Answer v = 2610 km s⁻¹
Δλ = 662.0 - 656.3 = 5.7 nm. v ≈ c × Δλ ÷ λ = 3.00 × 10⁸ × 5.7 ÷ 656.3 = 2.61e+03 km s⁻¹.
- Got 2.61 × 10⁶ km s⁻¹? That is the speed in m s⁻¹. Divide by 1000 to give km s⁻¹: v = 2.61e+03 km s⁻¹.
- Got 3.03 × 10⁵ km s⁻¹? You used the ratio of wavelengths. Use the fractional change: v = c × Δλ ÷ λ = c × 5.7 ÷ 656.3 = 2.61e+03 km s⁻¹.
- Using the right equation1 mark
Which observation is the strongest evidence for the Big Bang model?
- A The existence of white dwarfs.
- B The cosmic microwave background radiation.
- C The orbital period of the Moon.
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Answer B: The cosmic microwave background radiation.
The CMB is relic radiation from an early hot universe, now cooled to about 2.7 K, as the Big Bang model predicts.
- Why not A? White dwarfs are an end stage of stellar evolution and do not test models of the universe's origin.
- Why not C? The Moon's orbit tests gravity, not the origin of the universe.
- Using the right equation1 mark
Why are Type 1a supernovae used as standard candles?
- A They emit only X-rays.
- B They are the closest stars to Earth.
- C They all reach a similar peak luminosity.
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Answer C: They all reach a similar peak luminosity.
A white dwarf exploding near the Chandrasekhar limit gives a predictable peak luminosity, so the distance can be found from the observed flux.
- Why not A? They emit across the spectrum; their usefulness is the consistent peak luminosity.
- Why not B? Many are very distant; the key property is their known luminosity, not their closeness.