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Theme B — The Particulate Nature of Matter

B.1.15 Wien’s Displacement Law — IB Physics HL Revision Notes & Topical Questions

5 min read 9 parts Lesson 17 of 53 1 quiz

📚 IB Physics HL Hub / Topical Revision
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Lesson summary

B.1.15 Wien’s Displacement Law — IB PHYSICS SL notes: Use λmaxT = 2.90 × 10⁻³ m K to find the temperature of a black body from its peak wavelength.Black-body curve — a plot of intensity against wavelength rises from zero at short wavelengths to a peak at λmax and then falls with …

  • Higher temperature
  • Doubling T
  • Temperature units
  • Heating an object
  • Human body
  • Rigel and Betelgeuse

Part 1 of 7Black-body spectra

Black-body curve
  • Black-body curve a plot of intensity against wavelength rises from zero at short wavelengths to a peak at λmax and then falls with a long tail.
Higher temperature
  • Higher temperature the area under the curve increases (in proportion to T4), the peak moves to a shorter wavelength and the intensity rises at every wavelength.
Curves
  • Curves curves for different temperatures never cross.

Part 2 of 7Wien's displacement law

Statement
  • Statement the black-body curve peaks at a wavelength inversely proportional to the absolute temperature, λmax ∝ 1/T.
Equation
  • λmaxT = 2.90 × 10−3 m K.
  • λmax is the wavelength of greatest intensity in m.
  • T is the surface temperature in K.
Doubling T
  • Doubling T it halves the peak wavelength.
Temperature units
  • T is in kelvin, so convert from °C first.

Part 3 of 7Colour and temperature

Star colourTemperature / K
Blueabove 33 000
Blue-white10 000 to 30 000
White7500 to 10 000
Yellow-white6000 to 7500
Yellow5000 to 6000
Orange3500 to 5000
Redbelow 3500
Heating an object
  • Heating an object the peak moves from the infrared to red, then white, then blue and into the ultraviolet.
Examples
  • Examples a star at 3500 K peaks at 830 nm and looks red;
    • the Sun at 5800 K peaks near 500 nm;
    • a star at 20 000 K peaks at 145 nm in the ultraviolet.
Human body
  • Human body at 310 K the peak is near 9.4 μm in the infrared, which is why thermal imaging sees people in the dark.
Rigel and Betelgeuse
  • Rigel peaks at 263 nm and is hot (about 11 000 K); Betelgeuse peaks at 828 nm and is cool (about 3500 K).
Caution
  • Caution the apparent colour depends on the light in each part of the visible spectrum, not only on the peak.

Part 4 of 7Combining with other laws

1Step 1
  • Step 1 measure b and d to find L.
2Step 2
  • Step 2 measure λmax to find T.
3Step 3
  • Step 3 find R from L = 4πσR2T4.
4Why it works
  • Why it works stars are close to black bodies, with absorption lines superimposed on the continuous curve.
5Absorption lines
  • Absorption lines they come from the cooler outer atmosphere and give information about composition without moving the peak much.

Part 5 of 7Quantum origin

Ultraviolet catastrophe
  • Ultraviolet catastrophe classical physics predicted a divergence at short wavelengths, but experimental curves fall to zero.
Planck
  • Planck he proposed that energy is emitted in quanta, E = hf,
  • which began quantum theory.
    What the symbols mean: E = energy of one photon (J) · h = Planck constant (6.63 × 10−34 J s) · f = frequency (Hz)
Wien's law
  • Wien's law it follows from Planck's correct formula.

Part 6 of 7Reading spectra

Two curves
  • Two curves the curve with its peak at the shorter wavelength is the hotter, and it lies above the other at every wavelength.
Area
  • Area the hotter curve has the larger area, in line with L ∝ T4.
Calculation
  • Calculation convert nanometres to metres and state the temperature in kelvin.
Plausibility
  • Plausibility stellar temperatures between about 2500 K and 40 000 K are reasonable.
Approximation
  • Approximation the law is approximate for stars because they are not perfect black bodies.

Part 7 of 7More from the specification

1
Blackbody emission from celestial solids
  • Blackbody emission from celestial solids radiant energy emission peaks correlate with surface temperature across incandescent solids and planetary Earth surfaces.
2
Wien's Displacement Law for Black-Body Radiation
  • Wien's law states that the peak wavelength lambda_max of electromagnetic radiation emitted by an ideal black-body substance is inversely proportional to its thermodynamic temperature T: lambda_max = b / T.
3
Specific Heat Capacity in Calorimetry
  • When a heated solid is immersed into liquid water, thermal energy transfers between particles until thermal equilibrium is established, governed by Q = m * c * Delta T with zero net energy lost.
    • (such as a block of copper)
4
Specific Latent Heat During Phase Changes
  • The specific latent heat L of a substance is the thermal energy per unit mass required to change its physical state at constant temperature (Q = m * L),
  • where latent heat of fusion breaks lattice bonds and vaporisation separates liquid particles.
5
Thermal Radiation Emission Spectra
  • As the temperature of a glowing substance increases, the total intensity of emitted radiation increases drastically while the peak of the spectral emission curve shifts to shorter, higher-energy wavelengths.
    • (I proportional to T4
6
Internal energy
  • Total random kinetic and potential energy of all particles.
7
Potential energy
  • Energy stored by the configuration of a system.
8
Density
  • Mass per unit volume.
9
Solid
  • State with a fixed shape and a fixed volume.
10
Fusion
  • Joining of light nuclei into a heavier one.
11
Kinetic energy
  • K = ½mv2, energy of motion.
12
Apparent brightness
  • The power received per unit area at the observer
13
Thermal equilibrium
  • Constant temperature because energy is absorbed and lost at equal rates
14
Phase change
  • Change of matter from one state to another
15
Thermal conductivity
  • Material constant relating the rate of conduction to the temperature gradient and area
16
Radiation
  • Transfer by electromagnetic waves, requiring no medium
17
Liquid
  • State with a fixed volume that takes the shape of its container.
18
Copper
  • Metal widely used for electrical wires.
19
Convection
  • Transfer of thermal energy by the movement of a heated fluid
20
Conduction
  • Transfer of thermal energy by lattice vibrations and free electrons
21
Molecule
  • Tiny particle of the fluid, too small to be seen.
22
Luminosity
  • The total power of radiation emitted by a star.
23
Capacity
  • Charge a cell can supply, in A h or C.

Key terms

TermMeaning
Wien’s displacement lawλmaxT = 2.90 × 10−3 m K
Peak wavelengthWavelength at which a black body emits the greatest intensity
Black-body curveGraph of intensity against wavelength for a black body
Absorption lineDark line in a spectrum from absorption in a star's cooler atmosphere
QuantumDiscrete packet of energy, E = hf
Ultraviolet catastropheFailure of classical theory at short wavelengths

Avoid these mistakes

1
Using Celsius in Wien's law — use kelvin.
2
Forgetting to convert nanometres to metres — 1 nm = 10−9 m.
3
Thinking a hotter body peaks at a longer wavelength — it peaks at a shorter one.
4
Thinking the curves cross — a hotter body is higher at every wavelength.
5
Taking the peak colour as the apparent colour — the visible mix matters.

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