HSC Exam Practice

Sample response. (1) Continuous spectrum — source: hot solid, liquid or dense gas (e.g. a filament bulb, the solar interior). (2) Emission spectrum — source: hot thin gas (e.g. a neon sign, a hydrogen discharge tube). (3) Absorption spectrum — source: cool thin gas in front of a continuous source (e.g. the Sun’s cool atmosphere in front of its hot interior).

Marking notes. 1 mark per correctly matched spectrum type and source condition. Accept any valid physical example.

Sample response. In the quantum model, electrons in an atom can only exist in discrete (quantised) energy levels unique to each element [1]. An emission line is produced when an electron transitions from a higher energy level to a lower one, emitting a photon of energy E = hf = E_upper − E_lower [1]. Because the set of allowed energy levels differs for every element, the frequencies (and hence wavelengths) of emitted photons are unique to each element, producing a distinctive “fingerprint” pattern of lines [1].

Marking notes. 1 = electrons occupy discrete energy levels unique to each element; 1 = photon emitted when electron drops to lower level (E = hf = ΔE); 1 = unique energy-level spacing → unique line pattern per element.

Sample response. Redshift is the increase in the observed wavelength of light from a source that is moving away from the observer [1]. The formula is Δλ/λ₀ = v/c, where Δλ = λ_obs − λ₀ is the change in wavelength, λ₀ is the rest wavelength, v is the radial velocity of the source, and c is the speed of light [1]. This formula is valid for v ≪ c [1].

Marking notes. 1 = correct definition of redshift (wavelength increases, source receding); 1 = correct formula with all symbols defined; 1 = states limitation (non-relativistic, v ≪ c). Accept equivalent forms such as z = v/c.

Sample response. An emission spectrum (Kirchhoff’s Second Law) appears as bright coloured lines on a dark background, produced by a hot thin gas in which excited electrons drop to lower energy levels, emitting photons at specific wavelengths [2]. An absorption spectrum (Kirchhoff’s Third Law) appears as dark lines on a continuous rainbow background; it is produced when light from a continuous source passes through a cool thin gas, which absorbs photons at wavelengths corresponding to the same transitions as its emission lines [2].

Marking notes. 1 = emission: appearance (bright lines on dark) + Kirchhoff Second Law. 1 = emission: correct source condition (hot thin gas) and energy process (electron drops, emits). 1 = absorption: appearance (dark lines on continuous background) + Kirchhoff Third Law. 1 = absorption: correct source condition (cool gas + continuous source) and energy process (electron absorbs photon, rises to higher level).

Sample response. Astronomers use the radial velocity method (also called Doppler spectroscopy) [1]. An orbiting exoplanet gravitationally pulls the host star, causing the star to undergo a small circular motion about the common centre of mass. As the star alternately moves toward and away from Earth, its spectral lines undergo periodic blueshifts and redshifts [1]. By measuring the amplitude of these Doppler shifts (Δλ), astronomers calculate the star’s radial velocity using v = c Δλ/λ₀; the period of the oscillation gives the orbital period of the exoplanet [1].

Marking notes. 1 = names the technique (radial velocity / Doppler spectroscopy); 1 = explains the physical cause (gravitational wobble of the star induced by the planet); 1 = explains what is measured (Δλ of stellar spectral lines, periodic shifts give orbital period and planet mass estimate).

Sample response. The Sun’s hot, dense interior produces a continuous spectrum (Kirchhoff’s First Law) [1]. This light passes outward through the Sun’s cooler outer atmosphere (photosphere and chromosphere), which acts as a thin cool gas. By Kirchhoff’s Third Law, the cool atmospheric gas absorbs photons at wavelengths corresponding to the energy-level transitions of the elements present (H, Ca, Na, Fe, Mg, etc.), producing dark absorption lines [1]. These dark lines in the solar spectrum, called Fraunhofer lines, reveal the elemental composition of the Sun’s outer atmosphere [1].

Marking notes. 1 = hot dense interior produces continuous spectrum (Kirchhoff 1st law); 1 = cool outer atmosphere absorbs specific wavelengths (Kirchhoff 3rd law), producing dark lines; 1 = lines are called Fraunhofer lines and reveal the composition of the solar atmosphere (named elements acceptable).

Sample response (a) — completed table. NGC 4839: Δλ = +3.4 nm; v = 3.00×10⁵ × 3.4/656.3 = +1555 km s⁻¹. NGC 4874: Δλ = +4.9 nm; v = +2240 km s⁻¹. NGC 4889: Δλ = +2.1 nm; v = +960 km s⁻¹. NGC 4911: Δλ = +6.8 nm; v = +3109 km s⁻¹. All four galaxies are receding — indicated by positive Δλ. This means the Coma Cluster as a whole is moving away from Earth, consistent with the expansion of the universe (Hubble’s law) [1 per row = 4 marks + 1 for interpretation = 4 marks awarded here as part of the 8].

Sample response (b). Individual galaxies within a cluster move relative to the cluster’s centre of mass as they orbit within the cluster’s gravitational potential well [1]. Each galaxy’s radial velocity relative to Earth is the superposition of the whole-cluster recession velocity and the galaxy’s own orbital velocity within the cluster projected along the line of sight [1].

Sample response (c). The student’s claim is incorrect [1]. Velocity spread is expected in any gravitationally bound system — the galaxies are orbiting inside the cluster’s gravitational potential in the same way that stars orbit within a galaxy. A cluster breaks apart only if the individual galaxy velocities exceed the cluster’s escape velocity; velocity spread alone does not indicate escape [1].

Marking notes. Part (a): 1 mark per correctly calculated v (4 marks total); 1 mark for interpreting all four as receding and linking to cosmic expansion (or Hubble’s observation). Part (b): 1 = cluster recession + galaxy’s own orbit; 1 = explains velocity as superposition. Part (c): 1 = states claim is incorrect; 1 = explains bound orbits → velocity spread expected, not evidence of dissolution.

Sample response (a). Formula: v = c × (λ_obs − λ₀) / λ₀.

Star X: Δλ = 0; v = 0 m s⁻¹; No radial motion [1].

Star Y: Δλ = 394.5 − 393.3 = +1.2 nm; v = 3.00×10⁸ × 1.2×10⁻⁹ / 393.3×10⁻⁹ = +9.15×10⁵ m s⁻¹ (receding) [1].

Star Z: Δλ = 392.1 − 393.3 = −1.2 nm; v = 3.00×10⁸ × (−1.2×10⁻⁹) / 393.3×10⁻⁹ = −9.15×10⁵ m s⁻¹ (approaching) [1].

Sample response (b). Using v = +9.15×10⁵ m s⁻¹ for Star Y: Δλ = λ₀ × v/c = 656.3×10⁻⁹ × 9.15×10⁵/3.00×10⁸ = 656.3×10⁻⁹ × 3.05×10⁻³ = 2.0×10⁻⁹ m = 2.0 nm [1]. λ_obs = 656.3 + 2.0 = 658.3 nm [1].

Marking notes. 1 mark each for Stars X, Y, Z (velocity + direction); 1 mark for correct Δλ for Hα from Star Y; 1 mark for correct observed Hα wavelength for Star Y. Accept v in m s⁻¹ or km s⁻¹ providing units are correct. Accept ±1 in last significant figure due to rounding.

Sample response. Spectroscopy is arguably the most powerful technique in modern astrophysics because it can remotely probe the physical properties of objects too distant to visit. Kirchhoff’s three laws explain the three types of spectra observed. A hot, dense stellar interior produces a continuous blackbody spectrum (First Law). The star’s cooler outer atmosphere then produces dark absorption lines at wavelengths characteristic of the elements present — Fraunhofer lines in the Sun’s case — by Kirchhoff’s Third Law. By matching the positions of these dark lines to laboratory reference spectra, astronomers have determined that the Sun contains hydrogen (~75%), helium (~25%), and trace amounts of heavier elements such as calcium, iron, magnesium and sodium, all without ever collecting a physical sample. This is the single most important result obtained by spectroscopy: it established that the universe has a uniform chemical composition and that the same physical laws that apply on Earth apply throughout the cosmos. The Doppler effect extends spectroscopy into kinematics. When a star moves away from Earth, its spectral lines shift to longer wavelengths by Δλ/λ₀ = v/c. For example, if the Hα line (λ₀ = 656.3 nm) is observed at 657.6 nm, the recession velocity is v = 3.00×10⁵ × 1.3/656.3 = 594 km s⁻¹. Edwin Hubble used exactly this technique on spiral nebulae (now known to be external galaxies) in the 1920s, discovering that virtually all distant galaxies are redshifted and that recession velocity is proportional to distance — the first observational evidence for the expanding universe. The Doppler effect also reveals stellar dynamics in binary systems (periodic shifts identify orbital periods and companion masses) and enables the radial velocity method for exoplanet detection. In summary, Kirchhoff’s laws provide the theoretical basis for identifying what astronomical objects are made of, while the Doppler effect reveals how they are moving. Together, they turn starlight into a rich physical data set — a remarkable achievement given that no physical probe needs to leave Earth.

Marking criteria (7 marks). 1 = correctly explains how Kirchhoff’s Third Law accounts for absorption spectra in stellar atmospheres (continuous interior + cool atmospheric gas). 1 = correctly identifies spectroscopy’s role in determining stellar chemical composition using absorption line fingerprints (specific elements named or implied). 1 = states the Doppler shift formula (Δλ/λ₀ = v/c) and correctly interprets redshift as indicating recession. 1 = provides a correct quantitative example of Doppler shift calculation (any valid numbers consistent with formula). 1 = names Hubble’s discovery (galaxy recession, expanding universe) and links it to redshift spectroscopy as evidence. 1 = discusses a second astronomical application of Doppler spectroscopy (binary stars, exoplanet detection, or galaxy rotation). 1 = reaches an integrative evaluative conclusion that clearly addresses why spectroscopy is powerful as a tool — remote sensing of composition, velocity and structure without physical contact.