Black-Body Radiation & Spectral Classes — Quick Summary

Mr Toogood's Physics · Astrophysics

AQA 3.9.2.3 / 3.9.2.4

λ_max T = 2.9×10⁻³ mK

Wien's law

P = σAT⁴

Stefan's law

σ = 5.67×10⁻⁸

W m⁻²K⁻⁴

E = hf

Photon energy

Black-body radiation & Wien's law

Black-body radiation curves for three different temperatures

Hotter objects have a shorter peak wavelength and radiate more total power.

Drawing rules: steeper on the left; never touches or crosses the intensity axis; approaches (but never reaches) zero on the right.
Stars are excellent black-body approximations — they absorb all incident light and their spectrum matches the Planck curve closely.

λ_max T = 2.9×10⁻³ m·K

λ_max is the peak wavelength (highest intensity) — calling it the "maximum wavelength" is a common, mark-losing mistake.

Stefan's law

Diagram comparing a small hot star and a large cool star with the same absolute magnitude

Same power output, different temperature → the hotter star must be smaller.

P = σAT⁴ (A = 4πr²)

Since P is directly linked to absolute magnitude, two stars with equal M but different T must have different sizes — comparing diameters:

D_α/D_β = √(P_α/P_β) × (T_β²/T_α²)

Emission & absorption spectra

Cool gas absorbs photons, exciting electrons to higher levels — creating dark lines in an otherwise continuous spectrum. Excited gas emits photons of the same specific wavelengths as electrons de-excite — creating bright emission lines.

Hydrogen energy level diagram showing the Balmer series transitions to and from n=2

Balmer series: transitions to/from n=2 — the only series landing in the visible spectrum.

Only stars with substantial hydrogen in the n=2 state show strong Balmer lines — this depends on temperature, not just hydrogen abundance.

Stellar spectral classes (OBAFGKM)

Class	Colour	T / K	Key lines
O	Blue	25 000–50 000	He⁺, He, H
B	Blue	11 000–25 000	He, H
A	Blue-white	7 500–11 000	H (strongest)
F	White	6 000–7 500	Ionised metals
G	Yellow-white	5 000–6 000	Ion./neutral metals
K	Orange	3 500–5 000	Neutral metals
M	Red	<3 500	Neutral atoms, TiO

Mnemonic: "Oh Be A Fine Girl/Guy, Kiss Me."

Exam essentials

Key equations

λ_max T=2.9×10⁻³ m·K
P=σAT⁴
σ=5.67×10⁻⁸ W m⁻²K⁻⁴

Remember for OBAFGKM

Temperature range for each class.
Strongest absorption lines for each class.
Mnemonic: "Oh Be A Fine Girl/Guy Kiss Me."

Common slips

λ_max = peak wavelength, never "maximum wavelength."
Same T doesn't mean same L — size matters too (Stefan's law).
Balmer lines peak in A-class stars, not the hottest O-class — O stars ionise most hydrogen, leaving few electrons to absorb.