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Blackbody and Planck's law
Intermediate
Quantisation resolves ultraviolet catastrophe.
blackbodyPlanck's law B(λ,T) = (2hc²/λ⁵)/(e^{hc/λkT} − 1) describes the spectrum, peaking at λ_max = b/T. Quantisation removes the ultraviolet catastrophe.
The CMB follows it to 1 part in 10⁵.
Integrates to the Stefan–Boltzmann law.
In more detail
Planck's law gives the spectrum of blackbody radiation, I(λ,T) ∝ 1/(λ⁵(e^(hc/λkT) − 1)). It correctly predicts the peak and the shape of the curve at all wavelengths.
Real-world uses
- Estimating the temperature of stars and the early universe.
- Thermal imaging and calibration rely on Planck's law.
- Physicists use Planck's law to model the spectrum of stars and the cosmic microwave background.
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Frequently asked questions
How does it differ from classical theory?
Classical theory predicted infinite energy at short wavelengths, which Planck's law avoids.
Where is it used today?
In astrophysics, cosmology and infrared sensing.
What was the ultraviolet catastrophe?
The classical prediction of infinite energy at short wavelengths, which quantisation resolved.
Related topics in Quantum Mechanics
Lasers · Population inversion · Einstein coefficients · Quantum statistics of light · Quantum field theory intro · Feynman path integral