Astronomy & Space
Intermediate

Wien's Displacement Law

Peak emission wavelength of a blackbody.

Formula

λmax=bT\lambda_{max} = \frac{b}{T}

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Variables

bWien constant
TTemperature (K)

Example

The Sun peaks in green light (~500 nm), corresponding to its ~5800 K surface.

How it works

Wien’s displacement law tells you where a blackbody spectrum reaches its strongest emission: hotter objects peak at shorter wavelengths, while cooler objects peak at longer wavelengths. This happens because increasing temperature shifts the distribution of thermal radiation toward higher-energy photons, so the whole curve moves left as temperature rises. The constant b sets the scale of that inverse relationship and comes from the shape of the blackbody spectrum itself.

When to use it

Use this when you want to estimate the peak wavelength of thermal radiation from a star, planet, furnace, or any object that behaves approximately like a blackbody. It is especially useful for linking an object’s temperature to the part of the electromagnetic spectrum where it emits most strongly.

Worked example, step by step

Find the peak wavelength for a tungsten filament at 3000 K. Step 1: Write the law: λ_max = b / T Step 2: Use b = 2.898 × 10^-3 m·K and T = 3000 K Step 3: Substitute: λ_max = (2.898 × 10^-3 m·K) / (3000 K) Step 4: Calculate: λ_max = 9.66 × 10^-7 m Step 5: Convert to nanometres: 9.66 × 10^-7 m = 966 nm Final answer: The peak emission wavelength is about 966 nm, which is in the infrared.

Common mistakes to avoid

  • Using the temperature in °C instead of converting to kelvin first
  • Confusing the peak wavelength with the wavelength where the object emits the most total energy
  • Forgetting that the result is an approximation for a blackbody or near-blackbody, not every real object

Did You Know?

Wien's law is why hot iron glows red then white — hotter objects peak at bluer wavelengths.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026