HSC Exam Practice

Sample response. Big Bang nucleosynthesis is the formation of light nuclei from protons and neutrons during the first approximately three minutes after the Big Bang, when temperatures were high enough (~10⁹–10¹⁰ K) for nuclear fusion to occur. The two most abundant products were hydrogen (~75% by mass) and helium-4 (~25% by mass), with trace amounts of deuterium and lithium-7.

Marking notes. 1 mark for a correct definition including the time (~3 min) and high-temperature condition. 1 mark for correctly identifying hydrogen and its approximate mass fraction (~75%). 1 mark for correctly identifying helium-4 and its approximate mass fraction (~25%).

Sample response. The binding energy per nucleon curve peaks at iron-56, which has the highest binding energy per nucleon (~8.8 MeV) of all nuclei. Fusion of nuclei lighter than iron-56 moves up the curve toward the peak, producing products with greater binding energy per nucleon — energy is released. However, fusing nuclei beyond iron-56 would produce a product with a lower binding energy per nucleon (moving down the right side of the curve), meaning energy must be absorbed rather than released. Since stars are powered by energy-releasing fusion, they cannot sustain fusion beyond iron; the process becomes endothermic and the star’s core collapses rather than continuing to fuse.

Marking notes. 1 mark for correctly identifying the peak at iron-56 and its significance (~8.8 MeV/nucleon, most stable). 1 mark for explaining that fusion of nuclei lighter than Fe-56 releases energy (moves toward peak). 1 mark for explaining that fusion beyond Fe-56 absorbs energy (endothermic, moves away from peak), so stellar fusion cannot proceed.

Sample response. The r-process (rapid neutron capture) occurs in environments with an extremely high neutron flux, such as core-collapse supernova explosions and neutron star mergers. Nuclei absorb many neutrons faster than they can undergo beta decay, creating very neutron-rich unstable isotopes; these subsequently beta-decay to form stable heavy elements such as gold (Au) or uranium (U). The s-process (slow neutron capture) occurs in low- to intermediate-mass stars during the asymptotic giant branch (AGB) phase. Neutrons are captured one at a time with sufficient time between captures for beta decay, so intermediate nuclei remain near the valley of nuclear stability; representative elements include strontium (Sr) and lead (Pb).

Marking notes. 1 mark for correct description of r-process (rapid, high neutron flux, nuclei far from stability). 1 mark for a valid astrophysical site for r-process (supernovae or neutron star mergers) and a valid example element (Au, Pt, U, Ir — any r-process product). 1 mark for correct description of s-process (slow, low neutron flux, nuclei near stability, time for beta decay). 1 mark for a valid astrophysical site for s-process (AGB stars) and a valid example element (Sr, Ba, Pb — any s-process product).

Sample response. Iron-56 has the highest binding energy per nucleon of all nuclei (~8.8 MeV/nucleon). This implies that any nuclear reaction moving a nucleus closer to iron-56 releases energy: fusion of light nuclei (to the left of Fe-56 on the curve) produces more stable products by moving up toward the peak, releasing energy; similarly, fission of very heavy nuclei (to the right of Fe-56) also produces more stable products by moving toward the peak, releasing energy. Both processes converge on iron-56 as the endpoint of energy-releasing nuclear reactions.

Marking notes. 1 mark for correctly naming iron-56 as the peak. 1 mark for explaining fusion of light nuclei releases energy (moves toward Fe-56, higher BE/nucleon). 1 mark for explaining fission of heavy nuclei releases energy (also moves toward Fe-56, higher BE/nucleon).

Sample response. GW170817 was the first gravitational wave event identified as produced by a binary neutron star merger. Electromagnetic follow-up observations detected a kilonova — a short-duration optical and infrared transient. Spectroscopic analysis of the kilonova identified spectral signatures of freshly synthesised heavy r-process elements including strontium, gold, and platinum. This provided direct observational confirmation that neutron star mergers are a major site of r-process nucleosynthesis and thus a primary origin of elements heavier than iron, such as gold and platinum, alongside or possibly exceeding the contribution from core-collapse supernovae.

Marking notes. 1 mark for correctly identifying GW170817 as a neutron star merger detected via gravitational waves. 1 mark for describing the kilonova observation and its spectral evidence for r-process elements (strontium, gold, platinum — any valid heavy element). 1 mark for stating the implication: neutron star mergers confirmed as a major r-process/heavy-element production site.

Sample response. The mass defect (Δm) of a nucleus is the difference between the total mass of its constituent free protons and neutrons and the actual measured mass of the assembled nucleus. This “missing” mass was converted into binding energy when the nucleus formed, according to Einstein’s mass–energy relation $E = \Delta m c^2$; a larger mass defect per nucleon corresponds to greater nuclear stability. For helium-4 (two protons, two neutrons): $\Delta m = 4 \times 1.007276 - 4.001506 = 4.029104 - 4.001506 = 0.027598\ \text{u}.$

Marking notes. 1 mark for defining mass defect as the difference between the mass of free constituent nucleons and the actual nuclear mass. 1 mark for linking mass defect to binding energy via $E = \Delta m c^2$ and explaining the direction (mass converts to energy on formation). 1 mark for a correct worked expression yielding Δm ≈ 0.0276 u for ⁴He (accept 0.027598 or rounded).

Sample response (a). Mass defect: Δm = 3 × m(⁴He) − m(¹²C) = 3 × 4.001506 − 11.996709 = 12.004518 − 11.996709 = 0.007809 u. [1 — correct substitution. 1 — correct numerical answer. Accept 0.00781 u.]

Sample response (b). E = Δm × 931.5 = 0.007809 × 931.5 = 7.28 MeV [1 — correct formula; 1 — correct answer ~7.3 MeV; accept 7.2–7.4 MeV]. The positive value confirms the reaction is energetically favourable (exothermic): the carbon-12 product has a greater binding energy per nucleon than the three helium-4 nuclei, so the product is more tightly bound and energy is released [1 — interprets energy release in terms of binding energy].

Sample response (c). Helium nuclei carry charge +2 each, compared to +1 for protons, so the Coulomb (electrostatic) repulsion between two approaching helium nuclei is four times greater than between two protons (since $F \propto q_1 q_2 = 2 \times 2 = 4$ versus $1 \times 1$) [1 — correct Coulomb argument]. Therefore higher kinetic energies — achieved by higher core temperatures (~10⁸ K compared to ~10⁷ K for hydrogen fusion) — are required for helium nuclei to overcome this greater repulsion and reach the separation at which the strong nuclear force dominates [1 — links higher temperature to overcoming greater Coulomb barrier].

Marking criteria summary (7 marks): (a) 1 = correct formula (3m_He − m_C); 1 = correct Δm ≈ 0.00781 u. (b) 1 = E = Δm × 931.5; 1 = ~7.3 MeV; 1 = explains exothermic in terms of binding energy. (c) 1 = Coulomb repulsion greater for He (charge +2); 1 = higher temperature required to overcome greater Coulomb barrier.

Sample response. Astrophysical nucleosynthesis provides compelling evidence that the atoms composing the human body originated in stellar and cosmic environments. Hydrogen, the most abundant element in water and organic molecules (~63% of body atoms), is the product of Big Bang nucleosynthesis: protons formed in the first seconds of the universe and were never fully incorporated into heavier nuclei. Its overwhelming cosmic abundance (~75% by mass) reflects the limited fusion that occurred in the first three minutes, when the universe cooled too rapidly for proton capture beyond helium to proceed at scale. Carbon and oxygen, the backbone of all organic chemistry, were forged by stellar nucleosynthesis in low- to intermediate-mass stars. Carbon-12 is produced via the triple-alpha process (three  ⁴He → ¹²C), releasing ~7.3 MeV; oxygen-16 follows by alpha capture onto carbon. Both lie on the rising portion of the binding energy per nucleon curve well below the iron-56 peak, so their fusion from helium is exothermic and sustainably powers AGB stars. Iron itself, present in haemoglobin, was produced at the end point of massive stellar nucleosynthesis: silicon burning in cores of stars >8 M⊙ generates iron-56, which sits precisely at the top of the binding energy curve and marks the end of exothermic fusion. Further fusion is impossible; the core collapses and a supernova results, dispersing iron and all lighter products into the interstellar medium. Elements such as sulfur and calcium were produced in the oxygen- and silicon-burning shells of massive stars and ejected by supernovae. The strength of the observational evidence for these origins is substantial: stellar spectroscopy directly measures the elemental abundances in stellar cores and AGB star envelopes, confirming that carbon and barium (an s-process product) are enhanced in AGB stars’ outflows. The solar abundance pattern — showing peaks at s-process nuclei (Ba, Sr) and r-process nuclei (Au, Pt) — is reproduced to high precision by theoretical nucleosynthesis models. The kilonova GW170817 confirmed r-process element production in neutron star mergers. Taken together, the spectroscopic, isotopic, and gravitational-wave evidence strongly supports the conclusion that stellar and Big Bang nucleosynthesis are the origin of all elements in the human body, from the primordial hydrogen in water to the iron in blood.

Marking criteria (7 marks). 1 = correctly identifies and explains the origin of at least two biologically relevant elements with correct nucleosynthetic site (H from BBN; C/O from stellar AGB; Fe from massive star core). 1 = second element discussed correctly with site and mechanism. 1 = third element (or more) discussed correctly. 1 = correctly relates at least two elements to the binding energy curve (e.g. He to C is exothermic; Fe at peak limits fusion). 1 = correctly explains at least one energy argument (release of energy = product has higher BE/nucleon than reactants). 1 = cites at least two pieces of observational evidence and assesses their strength (stellar spectroscopy, solar abundance pattern, kilonova GW170817, isotopic abundances). 1 = reaches an explicit evaluative judgement integrating nucleosynthesis and evidence, concluding that the evidence is strong and multi-stranded.