Red-shift: Δλ/λ₀ = v/c
Light from a galaxy moving away is stretched to longer wavelengths — red-shift (its absorption lines shift to the red end). Formula (8.16P): where (m), = rest/lab wavelength (m), = recession speed (m/s), m/s. Critical: (the rest wavelength) always goes in the denominator — using the observed one loses the mark.
Hubble's law: further = faster
Observations show the further a galaxy, the greater its red-shift and so the faster it recedes — Hubble's law, ( = recession speed, = distance, km/s/Mpc; the exact value is not required at IGCSE). Crucially, galaxies are moving away from each other, not just from Earth — the universe itself is expanding. Running time backwards, all matter converges on a single point: the Big Bang.
Big Bang evidence: red-shift + CMB
The Big Bang: the universe began ~13.8 billion years ago from a single very hot, dense point and has expanded and cooled since. Two lines of evidence (8.14P): (1) cosmological red-shift — all distant galaxies are red-shifted, more so the further away, matching expansion from one origin; (2) cosmic microwave background (CMB) radiation — EM radiation from the hot early universe, now cooled to microwaves and arriving uniformly from all directions.
Drawn from real examiner reports.
Red-shift is a wavelength shift
Red-shift does not mean a galaxy "looks red" or "gets redder". The whole spectrum — its absorption lines — shifts to longer wavelengths. State it as: the received wavelengths are longer than those measured for the same element in a lab on Earth. Describing a colour change instead of a wavelength shift does not earn the definition mark.
June 2023 Paper 2P — candidates describing a colour change rather than a wavelength shift did not access the definition mark.
Put λ₀ in the denominator
In the denominator must be , the rest/lab wavelength. If a line is 630 nm in the lab and 645 nm from a galaxy, then nm and you divide by 630, not 645. Using the observed wavelength caps you at 1 mark.
June 2023 Paper 2P Q7(b)(ii) — the examiner named using the observed wavelength in the denominator as a reasonable misconception limited to 1 mark.
CMB radiation ≠ cosmic rays
CMB is low-energy microwave EM radiation arriving uniformly from all directions — the cooled remnant of the hot early universe, and evidence for the Big Bang. Cosmic rays are high-energy charged particles (mostly protons) from space. They are different phenomena; only the CMB is Big Bang evidence.
Chain the data to expansion
For "what does red-shift tell us?", do not just restate that light is red-shifted. Chain it: greater red-shift → greater recession speed → more distant galaxies recede faster → galaxies move away from each other → the universe is expanding. "Moving away from Earth" alone is not enough, and repeating the data scores zero.
June 2023 Paper 2P Q7(b)(iii) — the majority scored zero by restating red-shift rather than chaining to recession speed, distance and expansion; "away from Earth" was insufficient.
Red-shift vs blue-shift
Red-shift (wavelength increases) means the source moves away; blue-shift (wavelength decreases) means it moves towards you. All distant galaxies show red-shift, none blue-shift — which is why we say the universe is expanding, not contracting. Do not mix up the two directions.
λ_obs = λ₀ + Δλ (add it on)
When asked for the OBSERVED wavelength, add the shift to the rest wavelength: . Stopping at answers the wrong quantity. For a red-shift the observed wavelength must be larger than — a quick sanity check.
Chain: red-shift → expanding
For "why does red-shift support the Big Bang?", one linked step per mark: (1) received wavelengths longer than lab values → galaxies moving away; (2) more distant galaxies show greater red-shift, so recede faster; (3) galaxies move apart — the universe is expanding.
Red-shift calc: Δλ, then v
First find . Then use with in the denominator, and rearrange to . Give in m/s. Wavelength units cancel, so nm is fine if both match.
Identify λ₀ as the lab value first
Before substituting, label which number is the rest wavelength (measured in the lab, for the same element on Earth) and which is (from the galaxy). This one habit avoids the denominator trap that caps the mark.
Watch standard-form exponents
In cosmology sums the powers of ten are large — write them out and track the exponent. Dividing by increases the exponent: e.g. .
Red-shift equation (spec 8.16P):
| Symbol | Quantity | Unit |
|---|---|---|
| Change in wavelength () | m (or nm — must be consistent) | |
| Rest/laboratory wavelength | m (or nm) | |
| Recession speed of the galaxy | m/s | |
| Speed of light () | m/s |
Hubble's law (qualitative at IGCSE):
where = recession speed (km/s), = distance to galaxy (Mpc), = Hubble constant. At IGCSE you must know the relationship ( proportional to ) but do not need to memorise .
Define red-shift.
A hydrogen spectral line has a rest wavelength of 486 nm when measured in a laboratory. In the spectrum of a distant galaxy, the same spectral line is measured at 492 nm.
Calculate the change in wavelength . [1 mark]
