Wien's displacement law describes how the peak wavelength of light emitted by a hot object depends on its temperature. It is especially important for understanding blackbody radiation, which is the ideal pattern of electromagnetic radiation from an object that absorbs and emits perfectly. As temperature increases, the brightest part of the emitted spectrum moves toward shorter wavelengths.
This helps explain why cool stars look red, hotter stars look white or blue, and very hot objects can glow beyond the visible range.
Understanding Physics: Wien's Displacement Law
Every warm object sends out radiation across a broad range of wavelengths. Its spectrum is a curved distribution, not one single wavelength. The peak marks the wavelength with the greatest emitted intensity, but nearby wavelengths are still present.
A heated metal bar can therefore give off red, orange, and yellow light at the same time. As it becomes hotter, the balance changes.
Shorter wavelengths become much stronger compared with longer ones. This is why the visible colour changes gradually rather than jumping from red straight to blue.
Temperature must be measured on the Kelvin scale for this relationship to work. Kelvin starts at absolute zero, the lowest possible thermal temperature. A change of one kelvin has the same size as a change of one degree Celsius, but the zero points differ.
Room temperature is roughly 293 kelvin, while the surface of the Sun is close to 5800 kelvin. At room temperature, an object's strongest radiation is in infrared.
People cannot see this radiation, though infrared cameras can detect it. A stove element becomes visible only after it is hot enough for a noticeable part of its spectrum to enter the red region.
The law helps scientists estimate temperatures when direct measurements are impossible. Astronomers measure the wavelength near the peak of a star's spectrum, then use the relationship to calculate an approximate surface temperature. This method has limits.
Real stars contain gases that absorb particular wavelengths and create dark spectral lines. Dust between Earth and a star can scatter blue light more strongly, making the star appear redder.
A measured colour is therefore not always a direct temperature reading. Scientists use the full spectrum and other evidence to improve their estimates.
When solving problems, pay close attention to units. Wavelength may be given in metres, nanometres, or micrometres. These units differ by very large factors, so a missed conversion produces a very wrong temperature.
The temperature must be in kelvin, not Celsius. It is useful to check whether an answer is physically sensible. A cool human body should have a peak in infrared, while a very hot star should peak at a much shorter wavelength.
Remember that peak wavelength describes the strongest part of the emission, not the only radiation produced. This distinction explains why an object can emit infrared even when it looks blue or white.
Key Facts
- Wien's displacement law: lambda_max = b / T
- Wien's constant: b = 2.898 x 10^-3 m K
- lambda_max is the wavelength where the blackbody spectrum has maximum intensity.
- Higher temperature means smaller lambda_max because lambda_max is inversely proportional to T.
- Lower temperature means larger lambda_max, so cooler objects peak farther into the infrared or red part of the spectrum.
- Temperature from peak wavelength: T = b / lambda_max
Vocabulary
- Blackbody
- An ideal object that absorbs all incoming radiation and emits radiation with a spectrum determined only by its temperature.
- Peak wavelength
- The wavelength at which an object emits the greatest intensity of radiation.
- Wien's displacement law
- A law stating that the peak wavelength of blackbody radiation is inversely proportional to the object's absolute temperature.
- Kelvin
- The SI unit of absolute temperature, where 0 K represents absolute zero.
- Spectrum
- The range of wavelengths or frequencies of electromagnetic radiation emitted or absorbed by an object.
Common Mistakes to Avoid
- Using Celsius instead of Kelvin, which is wrong because Wien's law requires absolute temperature in kelvin.
- Thinking hotter objects peak at longer wavelengths, which is wrong because lambda_max = b / T shows that peak wavelength decreases as temperature increases.
- Confusing peak wavelength with total brightness, which is wrong because Wien's law gives the location of the maximum, not the total emitted power.
- Assuming a star's visible color exactly equals its peak wavelength, which is wrong because stars emit a broad spectrum and human color perception combines many wavelengths.
Practice Questions
- 1 A star has a surface temperature of 5800 K. Use lambda_max = b / T with b = 2.898 x 10^-3 m K to find its peak wavelength in meters and nanometers.
- 2 An object has peak emission at 1.0 x 10^-6 m. What is its temperature in kelvin?
- 3 Two stars have temperatures of 3500 K and 12000 K. Explain which star would appear redder, which would appear bluer, and why Wien's displacement law predicts this.