HSC Exam Practice

Sample response. All electromagnetic waves (1) travel at the speed of light \(c = 3.00 \times 10^8\) m/s in a vacuum, and (2) are transverse waves — the oscillating electric and magnetic fields are perpendicular to the direction of propagation and to each other.

Marking notes. 1 mark for stating all EM waves travel at \(c = 3.00 \times 10^8\) m/s in vacuum (must include numerical value). 1 mark for any second correct shared property: e.g. transverse nature, no medium required, obey \(c = f\lambda\), consist of oscillating E and B fields. Accept any two valid shared properties if the speed of light is included for one mark.

Sample response. Frequency (\(f\)) is the number of complete wave cycles passing a fixed point per second, measured in hertz (Hz). Wavelength (\(\lambda\)) is the distance between successive crests of a wave, measured in metres (m). For EM waves in a vacuum, they are related by \(c = f\lambda\), where \(c = 3.00 \times 10^8\) m/s, showing that frequency and wavelength are inversely proportional at constant \(c\).

Marking notes. 1 mark for a correct definition of frequency including the symbol \(f\) and unit Hz. 1 mark for a correct definition of wavelength including the symbol \(\lambda\) and unit m. 1 mark for stating \(c = f\lambda\) with both symbols identified, and noting that \(c\) is constant in vacuum.

Sample response. \(\lambda = c/f = 3.00 \times 10^8 / (1800 \times 10^6) = 3.00 \times 10^8 / 1.800 \times 10^9 = 0.167\) m (to 3 s.f.).

Marking notes. 1 mark for correct substitution with 1800 MHz correctly converted to \(1.800 \times 10^9\) Hz. 1 mark for correct answer 0.167 m (accept 16.7 cm). Penalise if answer is not given to 3 significant figures as instructed.

Sample response. By \(E = hf\), photon energy is directly proportional to frequency. Gamma rays have extremely high frequency (\(f \sim 10^{20}\) Hz), so each photon carries energy of order \(10^{-14}\) J (tens of MeV), far exceeding the ionisation energies of biological molecules (~4–25 eV). These photons can eject electrons from atoms (ionisation), break chemical bonds, and cause DNA strand breaks that lead to cell death or cancer. Infrared photons (\(f \sim 10^{13}\) Hz) carry energies of order \(10^{-20}\) J (~0.1 eV), which is 10\(^7\) times less than a gamma photon and insufficient to ionise atoms. At the same intensity (same total power), IR delivers far more photons per second, but each photon is too weak to ionise — the effect is gentle surface heating only.

Marking notes. 1 mark for correctly stating that \(E = hf\) means gamma photons (higher \(f\)) have vastly higher energy per photon than IR photons. 1 mark for explaining ionisation: gamma photons have enough energy to remove electrons from atoms/break chemical bonds; IR do not. 1 mark for explicitly linking ionisation to biological hazard (DNA damage, cancer) and distinguishing the mechanism from mere heating (IR effect).

Sample response. (a) Speed in fibre: \(v = c/n = 3.00 \times 10^8 / 1.50 = 2.00 \times 10^8\) m/s. (b) Wavelength in fibre: \(\lambda' = \lambda/n = 500/1.50 = 333\) nm. Frequency does NOT change. The frequency is determined by the source (the oscillation rate of the emitting atom) and cannot be altered by the medium. Since \(v = f\lambda'\), both \(v\) and \(\lambda'\) decrease by the same factor \(n\), keeping \(f\) constant: \(f = v/\lambda' = 2.00\times10^8/333\times10^{-9} = 6.00\times10^{14}\) Hz, identical to \(c/\lambda_{\text{vacuum}} = 3.00\times10^8/500\times10^{-9} = 6.00\times10^{14}\) Hz.

Marking notes. 1 mark for \(v = c/n = 2.00 \times 10^8\) m/s (part a). 1 mark for \(\lambda' = \lambda/n = 333\) nm (part b). 1 mark for correctly stating frequency does not change. 1 mark for a clear explanation: frequency is set by the source; only speed and wavelength change by factor \(n\).

Sample response. The flaw is equating speed with biological effect. Although all EM waves travel at \(c\) in a vacuum, what determines their effect on matter is the energy carried per photon, not their speed. By \(E = hf\), photon energy depends on frequency: gamma rays (\(f \sim 10^{20}\) Hz, \(E \sim 10^{-14}\) J per photon) carry roughly 10\(^{26}\) times more energy per photon than radio waves (\(f \sim 10^6\) Hz, \(E \sim 10^{-27}\) J per photon). Gamma photons can ionise atoms and cause DNA damage; radio photons lack the energy to cause any ionisation at all. The speed is the same; the consequences are vastly different.

Marking notes. 1 mark for correctly identifying the flaw: speed does not determine biological effect — photon energy does. 1 mark for applying \(E = hf\): gamma rays have much higher frequency and therefore much higher photon energy than radio waves. 1 mark for explaining the consequence: gamma photons ionise atoms/break bonds; radio photons do not — so their biological effects are fundamentally different despite equal speeds.

Sample response (a). Peak wavelength: ~500 nm (read from graph). \(f = c/\lambda = 3.00\times10^8/500\times10^{-9} = 6.00\times10^{14}\) Hz. \(E = hf = 6.63\times10^{-34}\times6.00\times10^{14} = 3.98\times10^{-19}\) J. In eV: \(3.98\times10^{-19}/1.60\times10^{-19} = 2.49\) eV.

Marking notes (a). 1 mark for reading peak as ~500 nm (accept 480–520 nm). 1 mark for correct \(f\) calculation. 1 mark for correct \(E\) in eV (accept 2.4–2.6 eV for any peak value in the accepted range).

Sample response (b). The atmosphere absorbs UV below 300 nm primarily because ozone (O\(_3\)) in the stratosphere absorbs these high-energy photons — UV-C (\(\lambda <\) 280 nm) and most UV-B (\(280–315\) nm) are absorbed before reaching the surface. This is critical for life on Earth: UV-C and UV-B photons carry energies of 4–12 eV per photon, sufficient to ionise molecules and break DNA bonds. Without ozone layer absorption, this radiation would cause dramatically increased rates of skin cancer, cataracts, and genetic mutations in surface-dwelling organisms. The ozone layer is thus essential for the existence of life as we know it on Earth’s surface.

Marking notes (b). 1 mark for identifying ozone (stratospheric O\(_3\)) as the primary UV absorber below 300 nm. 1 mark for explaining the mechanism (high-energy UV photons are absorbed by ozone molecules before reaching the surface). 1 mark for describing the consequence: without this absorption, ionising UV would damage DNA and cause skin cancer / mass extinction of surface organisms.

Sample response (c). \(E_{400} = hc/\lambda = 6.63\times10^{-34}\times3.00\times10^8/400\times10^{-9} = 4.97\times10^{-19}\) J = 3.11 eV. \(E_{1200} = 6.63\times10^{-34}\times3.00\times10^8/1200\times10^{-9} = 1.66\times10^{-19}\) J = 1.04 eV. Ratio \(E_{blue}/E_{IR} = 3.11/1.04 = 3.0\) (blue photons are 3 times more energetic per photon). Implication: the 1200 nm IR photons carry only 1.04 eV — just below the 1.1 eV minimum needed to generate electron-hole pairs in silicon. These IR photons therefore cannot generate electricity in a silicon solar cell. The 400 nm blue photons (3.11 eV) easily exceed the threshold and are effective. Solar cells must match their bandgap to the peak of the solar spectrum to maximise efficiency.

Marking notes (c). 1 mark for correct \(E_{400}\) in eV. 1 mark for correct \(E_{1200}\) in eV and correct ratio (3.0, accept 2.9–3.1). 1 mark for correct implication: IR photons at 1200 nm are below the 1.1 eV threshold and cannot generate electricity; blue photons can (with reference to the threshold value given).

Sample response. The claim is incorrect. Although all electromagnetic waves travel at \(c = 3.00 \times 10^8\) m/s in a vacuum, their biological effects are determined by the energy carried per photon, not by their speed. The fundamental relationship is \(E = hf = hc/\lambda\): photon energy increases with frequency and decreases with wavelength. The EM spectrum spans an enormous range of photon energies — radio waves at \(10^6\) Hz carry only \(\sim 10^{-27}\) J per photon (\(\sim 10^{-8}\) eV), while gamma rays at \(10^{20}\) Hz carry \(\sim 10^{-13}\) J per photon (\(\sim 10^6\) eV) — a factor of 10\(^{26}\) difference. The key biological threshold is ionisation: a photon must carry at least 10–15 eV (roughly \(10^{-18}\) J) to remove an electron from an atom or break a covalent chemical bond. Radiation above this threshold is called ionising radiation; below it, non-ionising. X-rays and gamma rays are ionising: each photon carries enough energy to create free radicals, break DNA strands, and disrupt cell function, potentially causing cancer or cell death. This is why medical X-ray imaging (used widely in Australian hospitals for fracture diagnosis and chest screening) requires strict dose limits and lead shielding — accumulated ionising dose causes long-term cancer risk. Radio waves and microwaves are non-ionising: individual photons cannot break bonds. Their only physiological effect at high intensity is heating of tissue through dielectric absorption (the principle of a microwave oven). The Australian Radiation Protection and Nuclear Safety Agency (ARPANSA) sets exposure limits for radio frequency fields based on specific absorption rate (heating), not ionisation risk. Visible light photons (1.8–3.1 eV) are also non-ionising but can cause photochemical reactions in the retina (useful for vision) or, in excess UV (3–5 eV), photochemical damage to skin DNA — the cause of skin cancer, the most common cancer in Australia. The ozone layer protects the surface from the most energetic UV-C (\(>\)5 eV), leaving only UV-A and UV-B to reach ground level. In summary, the claim is fundamentally flawed: identical speeds do not imply identical effects. The biologically critical quantity is photon energy (\(E = hf\)), which varies by 26 orders of magnitude across the spectrum. Ionising radiation (X-rays, gamma rays) poses serious cancer risks at low doses, while radio waves pose only thermal risks at very high intensities. Speed is irrelevant to biological hazard.

Marking criteria (8 marks). 1 = correctly identifies the flaw in the claim: speed is irrelevant; photon energy determines biological effect. 1 = states and applies \(E = hf\): explains that energy increases with frequency, and quantifies or compares the energy range across the spectrum. 1 = defines ionisation correctly: a photon must carry sufficient energy to remove an electron or break a chemical bond; identifies the ionising threshold (~10 eV). 1 = correctly classifies ionising radiation (X-rays, gamma rays) and non-ionising (radio, microwave, IR, visible) with reference to \(E = hf\). 1 = first named Australian healthcare or environmental science example used correctly to illustrate hazard or safety (e.g. medical X-ray dose limits at Australian hospitals / ARPANSA RF exposure standard / ozone layer absorbing UV-C over Australia). 1 = second named Australian example (e.g. skin cancer rates in Australia linked to UV photon energy / UV index warnings from Bureau of Meteorology / radiotherapy using gamma rays at Australian cancer centres). 1 = integrates the \(E = hf\) relationship with a comparison of at least two specific spectral regions using calculated or quoted photon energy values. 1 = reaches an explicit evaluative judgement: rejects the claim with a clear, logically consistent conclusion that references both the speed (constant) and the energy (varies enormously) to distinguish the two.