Lessons 6–10 cover stellar evolution, nucleosynthesis, the HR diagram, spectroscopy and stellar classification, and supernovae/neutron stars. This checkpoint assesses your understanding of how elements are produced, how stars evolve, and how astronomers analyse starlight to determine stellar properties.
Star formation, main sequence, red giants, white dwarfs, Chandrasekhar limit
BBN, binding energy curve, r-process, s-process, element origins
Luminosity vs temperature, main sequence, giants, white dwarfs, cluster ages
Spectral types, absorption/emission spectra, Doppler shift, radial velocity
Type Ia vs Type II, neutron stars, pulsars, GW170817
15 questions — instant feedback
Q1. During the main sequence, a star fuses:
Correct: B. Main sequence stars fuse hydrogen into helium in their cores.
Q2. A star with initial mass $5 M_{\\odot}$ will end as a:
Correct: C. Stars with initial mass $< 8 M_{\\odot}$ become white dwarfs.
Q3. The binding energy per nucleon peaks at:
Correct: A. Iron-56 has the highest binding energy per nucleon (~8.8 MeV).
Q4. Elements heavier than iron are primarily produced by:
Correct: D. The r-process in supernovae and neutron star mergers builds nuclei beyond iron.
Q5. A star has $T = 3,500$ K and $L = 10,000 L_{\\odot}$. Using $L = 4\\pi R^2 \\sigma T^4$, its radius is approximately:
Correct: C. $R/R_{\\odot} = \\sqrt{10000} \\times (5800/3500)^2 = 100 \\times 2.75 \\approx 275$. Closest to 100 (approximate).
Q6. On the HR diagram, white dwarfs are located:
Correct: B. White dwarfs are hot (left) but dim (below), indicating small radius.
Q7. A star shows strong hydrogen Balmer lines and weak metal lines. Its spectral type is most likely:
Correct: A. A-type stars ($7,500-10,000$ K) show strong hydrogen Balmer lines.
Q8. A spectral line at 500 nm is observed at 505 nm. The object's radial velocity is approximately:
Correct: D. $z = 5/500 = 0.01$. $v = 0.01 \\times 3\\times10^5 = 3,000$ km/s away (redshift).
Q9. Type Ia supernovae are standard candles because:
Correct: B. All Type Ia SNe occur at the Chandrasekhar limit, giving nearly identical peak luminosities.
Q10. A neutron star is supported against collapse by:
Correct: C. Neutron degeneracy pressure from the Pauli exclusion principle supports neutron stars.
Q11. The s-process occurs primarily in:
Correct: A. The s-process (slow neutron capture) occurs in asymptotic giant branch stars.
Q12. A $10 M_{\\odot}$ star has main sequence lifetime approximately:
Correct: D. $t = 10 \\times 10^{-2.5} \\approx 0.03$ Gyr = 30 Myr.
Q13. Why does a massive star's iron core collapse rather than expanding when fusion stops?
Correct: B. Fusion provides the outward thermal/radiation pressure that balances gravity. When fusion stops, gravity dominates and the core collapses.
Q14. The main sequence turn-off point of a star cluster at $2 M_{\\odot}$ indicates the cluster's age is approximately:
Correct: C. $t = 10 \\times 2^{-2.5} = 10/5.66 \\approx 1.8$ Gyr.
Q15. GW170817 confirmed that neutron star mergers produce heavy elements because:
Correct: A. The optical/infrared afterglow showed spectral features of freshly synthesized r-process elements like gold and platinum.
5 questions — model answers revealed
SAQ 1. (a) Distinguish between the s-process and r-process of nucleosynthesis. (b) Explain why elements heavier than iron cannot be produced by fusion in stellar cores. (c) Identify the astrophysical sites where gold and uranium are primarily produced. (4 marks)
Model answer (4 marks):
(a) s-process: slow neutron capture in AGB stars; neutrons captured one at a time with time for beta decay (0.5 mark). r-process: rapid neutron capture in supernovae and neutron star mergers; multiple neutrons captured before beta decay (0.5 mark).
(b) Iron-56 has maximum binding energy per nucleon (0.5 mark). Fusing beyond iron requires energy input (endothermic) rather than releasing it (0.5 mark).
(c) Gold and uranium are primarily produced by the r-process in supernovae and neutron star mergers (1.5 marks). The 2017 GW170817 event confirmed neutron star mergers as a major site.
SAQ 2. (a) Calculate the radius of a star with $L = 100 L_{\\odot}$ and $T = 5,800$ K (same as Sun). (b) A star has $T = 3,000$ K and $L = 1,000 L_{\\odot}$. Calculate its radius relative to the Sun. (c) Explain why this star must be a red giant. (4 marks)
Model answer (4 marks):
(a) From $L = 4\\pi R^2 \\sigma T^4$, at same $T$, $R \\propto \\sqrt{L}$. So $R = \\sqrt{100} = 10 R_{\\odot}$ (1 mark).
(b) $R/R_{\\odot} = \\sqrt{1000} \\times (5800/3000)^2 = 31.6 \\times 3.74 \\approx 118$ (1.5 marks).
(c) The star is much cooler than the Sun but over 100 times larger in radius. This combination of low temperature and enormous size places it in the red giant region of the HR diagram (1.5 marks).
SAQ 3. (a) Explain the difference between absorption and emission spectra. (b) Describe how a star's spectral type is related to its surface temperature. (c) A star shows strong TiO molecular bands. Predict its spectral type, colour, and approximate temperature. (d) Calculate the radial velocity if the H$\\alpha$ line ($656.3$ nm) is observed at $653.3$ nm. (4 marks)
Model answer (4 marks):
(a) Absorption: continuous spectrum with dark lines from cooler gas absorbing specific wavelengths (0.5 mark). Emission: bright lines on dark background from hot gas emitting at specific wavelengths (0.5 mark).
(b) Spectral type depends on temperature because temperature determines which ions/atoms are present and which electron transitions are populated (0.5 mark).
(c) TiO bands indicate spectral type M, red colour, $T < 3,700$ K (0.5 mark).
(d) $z = (653.3 - 656.3)/656.3 = -0.00457$ (0.5 mark). $v = -0.00457 \\times 3\\times10^5 = -1,370$ km/s (approaching) (1 mark).
SAQ 4. (a) Distinguish between Type Ia and Type II supernovae, including their progenitors, explosion mechanisms, and remnants. (b) Explain why Type Ia supernovae are useful as standard candles. (c) Calculate the density of a neutron star with $M = 1.4 M_{\\odot}$ and $R = 12$ km. (d) Explain the significance of the Tolman-Oppenheimer-Volkoff limit. (5 marks)
Model answer (5 marks):
(a) Type Ia: WD accretion → Chandrasekhar limit → thermonuclear runaway; no remnant (1 mark). Type II: massive star iron core collapse → shock bounce → explosion; leaves NS or BH (1 mark).
(b) All Type Ia SNe explode at same mass, giving same peak luminosity; comparing apparent to absolute magnitude gives distance (1 mark).
(c) $\\rho = 2.8\\times10^{30}/(4/3 \\pi (1.2\\times10^4)^3) \\approx 3.9\\times10^{17}$ kg/m³ (1 mark).
(d) The TOV limit (~$3 M_{\\odot}$) is the maximum mass supported by neutron degeneracy pressure. Above this, collapse to a black hole is inevitable (1 mark).
SAQ 5. (a) Outline the process of Big Bang nucleosynthesis and explain why it produced only hydrogen, helium, and trace lithium. (b) Describe the stellar nucleosynthesis pathway from hydrogen to iron in a massive star. (c) Explain why the binding energy per nucleon curve determines that fusion beyond iron is not energetically favourable. (d) Discuss how the observed abundances of elements in the solar system provide evidence for multiple nucleosynthetic processes. (5 marks)
Model answer (5 marks):
(a) In first ~3 minutes, $p + n \\rightarrow$ D, then D + D → He-3/He-4. Universe cooled below fusion temperature before heavier elements could form (1 mark).
(b) H → He (pp chain/CNO), He → C (triple-alpha), C → O, O → Ne, Ne → Mg, Mg → Si, Si → Fe. Progressive core burning at increasing temperatures (1.5 marks).
(c) Fe-56 has maximum binding energy per nucleon (~8.8 MeV). Fusing beyond Fe moves down the curve, decreasing binding energy per nucleon — this requires energy input (endothermic) (1.5 marks).
(d) H/He dominance matches BBN. C/O abundance matches stellar nucleosynthesis. Heavy element abundance (peaks at magic neutron numbers) matches r-process and s-process. No single process can explain all observed abundances (1 mark).