HSC Exam Practice

Sample response. Redshift is the increase in wavelength of electromagnetic radiation received from an object, caused by the object or space moving such that the distance between source and observer is increasing. The redshift parameter is defined as $z = (\lambda_{obs} - \lambda_{rest})/\lambda_{rest}$, where $\lambda_{obs}$ is the observed wavelength and $\lambda_{rest}$ is the laboratory (rest) wavelength.

Marking notes. 1 mark for a correct qualitative definition of redshift (wavelength increase / recession). 1 mark for the correct formula $z = (\lambda_{obs} - \lambda_{rest})/\lambda_{rest}$ written explicitly (accept $z = \Delta\lambda/\lambda_{rest}$).

Sample response. (1) Cosmological redshift and expansion: distant galaxies show spectral lines shifted to longer wavelengths; the amount of redshift is proportional to distance (Hubble’s law, $v = H_0 d$), indicating that space is expanding — consistent with the universe originating from a hot, dense singularity. (2) Cosmic Microwave Background: the universe is filled with uniform microwave radiation from all directions with a near-perfect black-body spectrum at 2.725 K; this is the cooled relic radiation predicted by the Big Bang from the epoch of recombination (~380 000 years after the Big Bang). (3) Primordial nucleosynthesis: the observed mass fractions of hydrogen (~75%), helium-4 (~25%), and trace deuterium and lithium in old, metal-poor environments match the predictions of Big Bang nucleosynthesis calculations for the observed baryon density.

Marking notes. 2 marks per pillar (1 for identifying the pillar and its key observation; 1 for linking it to a specific Big Bang prediction). Award 0 for a pillar stated without any observational detail.

Sample response. In the early universe, matter and radiation were in thermal equilibrium: photons were continuously absorbed and re-emitted by the hot, dense plasma, causing the radiation to take on a perfect black-body (Planck) spectrum characteristic of the equilibrium temperature [1]. When the universe cooled to ~3000 K (~380 000 years after the Big Bang), electrons combined with protons to form neutral hydrogen (recombination). Photons decoupled from matter and propagated freely, retaining the black-body spectral shape [1]. The expansion of the universe has since cooled this radiation by a factor of ~1100 to 2.725 K, implying the universe was once extremely hot and dense — consistent with the Big Bang model [1].

Marking notes. 1 mark for thermal equilibrium in the early universe producing a black-body spectrum. 1 mark for recombination/decoupling explanation. 1 mark for linking the current 2.725 K temperature to cooling by expansion, implying a hot dense early state.

Sample response. Doppler redshift is caused by the relative motion of the source through space away from the observer; the wavelength stretches because each successive wave crest is emitted from a slightly farther position [1]. Cosmological redshift is caused by the expansion of space itself stretching the wavelength of the photon as it travels; neither the galaxy nor the observer is moving through space, but the distance between them increases because the space metric is expanding [1]. For very distant galaxies ($z > 1$), recession “velocities” inferred from $v = cz$ can exceed $c$, which appears to violate special relativity. This is not a contradiction for cosmological redshift because it is space expanding, not matter moving through space faster than $c$ [1]. Additionally, the Doppler formula $v = cz$ is only valid for $z \ll 1$; for high-$z$ objects the correct relationship requires a relativistic (or general-relativistic) treatment that accounts for the expansion history of the universe [1].

Marking notes. 1 mark for Doppler = motion through space. 1 mark for cosmological = expansion of space stretching wavelength. 1 mark for noting that $v > c$ is possible for cosmological recession without violating SR. 1 mark for noting that $v = cz$ breaks down at high $z$ / requires relativistic treatment.

Sample response. Stars produce helium by fusing hydrogen, but the observed helium fraction of ~25% is too large to be explained by stellar processing alone [1]. If sufficient hydrogen had been burned in stars to produce this much helium, the resulting heavy-element (metal) abundance would be far higher than the very low metallicities observed in old, Population II stars and metal-poor halo gas clouds [1]. Furthermore, deuterium is destroyed by stellar fusion (it fuses at temperatures lower than those needed for hydrogen burning). The observed primordial deuterium abundance ($D/H \approx 2.6 \times 10^{-5}$) cannot have survived stellar processing; it must have been created in the first few minutes after the Big Bang, before any stars existed. This rules out stellar nucleosynthesis as the sole source of the light-element abundances [1].

Marking notes. 1 mark for identifying that 25% He is too high for stellar origin alone. 1 mark for the heavy-element overproduction argument (stars would leave too many metals). 1 mark for the deuterium destruction argument (D is destroyed in stars; its survival proves primordial origin).

Sample response (a). $z = (403.0 - 393.4)/393.4 = 9.6/393.4 = 0.0244$.

Marking notes (a). 1 mark for correct formula with correct values substituted and answer $z \approx 0.024$ (accept 0.0243–0.0244).

Sample response (b). $v \approx cz = 3.0 \times 10^5 \times 0.0244 = 7320$ km/s. $d = v/H_0 = 7320/70 = 104.6$ Mpc $\approx 105$ Mpc.

Marking notes (b). 1 mark for correct recession velocity ($v \approx 7300$–$7320$ km/s). 1 mark for correct distance ($d \approx 104$–$106$ Mpc). Accept rounding at each step.

Sample response (a) — two features (4 marks). Feature 1: The map is overwhelmingly uniform in temperature across all directions (the vast majority of the map shows the same grey tone); this near-perfect isotropy is evidence that the early universe was in thermal equilibrium at the time of recombination, consistent with the Big Bang prediction that the universe was once extremely hot and dense and homogeneous [1 identify + 1 link]. Feature 2: The tiny temperature fluctuations ($\Delta T/T \sim 10^{-5}$) are present as small light and dark patches; these anisotropies are predicted by the Big Bang model as quantum fluctuations in the early universe that have been stretched to cosmic scales — their angular scale and amplitude match Big Bang predictions precisely [1 identify + 1 link].

Sample response (b) — temperature fluctuations and structure (3 marks). The slightly denser (cooler) regions in the early universe had slightly greater gravitational attraction [1]. Over billions of years, these overdense regions attracted more matter, growing under gravity while underdense regions became voids [1]. The galaxy clusters and cosmic filaments we observe today are the gravitationally amplified descendants of these primordial fluctuations; the CMB anisotropy map is effectively a “blueprint” for the large-scale structure of the present universe [1].

Sample response (c) — steady-state assessment (3 marks). The claim is incorrect [1]. The steady-state model predicts no CMB at all because it requires no hot, dense early phase and therefore no relic thermal radiation [1]. In the steady-state model there is no mechanism to produce a uniform, isotropic background at a specific temperature, let alone the specific pattern of anisotropies whose angular power spectrum matches the Big Bang prediction. The observation of the CMB is therefore incompatible with the steady-state model and was a principal reason for its scientific abandonment after 1965 [1].

Marking notes summary. (a) 2 marks per feature (1 identify + 1 link to Big Bang). (b) 1 mark for gravity acting on overdensities; 1 mark for growth over time; 1 mark for connecting to present-day large-scale structure. (c) 1 mark for “incorrect” + justification; 1 mark for steady-state predicts no CMB; 1 mark for angular anisotropy pattern / fatal for steady-state.

Sample response. The Big Bang theory is supported by three independent pillars of evidence, each providing a self-consistent and quantitatively precise confirmation of the model. The first pillar is cosmological redshift and Hubble’s law: Hubble observed that all distant galaxies recede at velocities proportional to their distance ($v = H_0 d$, $H_0 \approx 70$ km/s/Mpc), with no preferred direction. This indicates that space itself is expanding, which, when traced backwards in time, implies the universe originated from an extremely compact state. The most distant galaxies known have $z > 10$, confirming that the expansion has been occurring for more than 13 billion years. No steady-state model can reproduce the systematic relationship between redshift and distance without invoking expansion. The second pillar is the CMB, discovered accidentally by Penzias and Wilson in 1965. The CMB has a near-perfect black-body spectrum at $T = 2.725$ K, arriving isotropically from all directions with $\Delta T/T \sim 10^{-5}$. The Big Bang model predicts that radiation decoupled from matter at recombination (~380 000 years after the Big Bang, $T \approx 3000$ K) and has since cooled to 2.725 K. The COBE, WMAP and Planck satellites have all confirmed this prediction to extraordinary precision. The third pillar is primordial nucleosynthesis: the Big Bang model predicts that in the first three minutes, protons and neutrons fused to form ~75% hydrogen and ~25% helium-4 by mass, with trace deuterium and lithium. These predictions depend on the baryon density; the measured D/H $\approx 2.6 \times 10^{-5}$ constrains this independently, and all nuclei abundances are consistent with a single baryon density — confirming a coherent, self-consistent model. The convergence of three completely independent observational techniques (spectroscopy of galaxies, microwave radiometry, and spectroscopy of metal-poor stars and gas clouds) all pointing to the same model with the same parameters is the strongest possible scientific validation. Each pillar alone could conceivably have an alternative explanation; the three together constrain the parameter space so tightly that no competing model survives. The limitations of the evidence include: (i) the CMB temperature measurements assume that the CMB is purely primordial; foreground emission from the Milky Way (visible as the central band in the anisotropy map) must be carefully subtracted, introducing potential systematic errors; (ii) helium abundance measurements in H II regions are subject to systematic modelling uncertainties; (iii) for very high-$z$ galaxies, the simple Hubble’s law approximation fails and distance estimates require a full cosmological model. To falsify the Big Bang model, one would need to observe a galaxy with a blueshift inconsistent with local motions, show that the CMB is not thermal (e.g. has spectral lines or discontinuities), or measure a light-element abundance that cannot be reconciled with any baryon density in a BBN calculation — none of these has been observed.

Marking criteria (7 marks). 1 = Pillar 1: redshift + Hubble’s law stated with correct formula and a specific quantitative detail ($H_0$, $z$ value, or $v \propto d$). 1 = Pillar 2: CMB temperature 2.725 K and black-body spectrum, linked to recombination prediction. 1 = Pillar 3: light-element abundances (He-4 ~25%, D/H) linked to BBN and baryon density. 1 = Convergence argument: three independent lines of evidence agree on the same model — stated explicitly with reasoning. 1 = At least one specific limitation of the evidence discussed (e.g. systematic error, foreground subtraction, measurement uncertainty). 1 = Concept of falsifiability applied correctly: states what observation(s) would falsify the Big Bang. 1 = Response uses precise scientific terminology throughout and integrates evidence into a coherent evaluative argument (not a list). Deduct marks if the student merely lists observations without evaluating their significance.