Blackbody Radiation Curves

Blackbody radiation curves show the spectral distribution of electromagnetic radiation emitted by a perfect blackbody at thermal equilibrium. These curves are fundamental to understanding quantum mechanics and stellar physics.

Interactive Visualization

Temperature: 5800 K

Show multiple temperature curves

Peak Wavelength (Wien's Law):

\lambda_{max} = 500

Total Power (Stefan-Boltzmann):

64.16

MW/m²

Wavelength (nm) vs Intensity - Interactive blackbody radiation curves

Planck's Law

The spectral radiance of blackbody radiation is given by Planck's law:

B_\lambda(T) = \frac{2hc^2}{\lambda^5} \frac{1}{e^{\frac{hc}{\lambda k_B T}} - 1}

Where:

$B_\lambda(T)$ is the spectral radiance
$h$ is Planck's constant (6.626 × 10⁻³⁴ J·s)
$c$ is the speed of light (3 × 10⁸ m/s)
$\lambda$ is the wavelength
$k_B$ is Boltzmann's constant (1.381 × 10⁻²³ J/K)
$T$ is the absolute temperature

Wien's Displacement Law

The wavelength of maximum emission is inversely proportional to temperature:

\lambda_{max} = \frac{b}{T}

Where KaTeX can only parse string typed expression m·K is Wien's displacement constant.

Temperature Examples

Sun (5778 K): Peak at 502 nm (green light)
Incandescent bulb (3000 K): Peak at 966 nm (near-infrared)
Human body (310 K): Peak at 9.3 μm (far-infrared)
Hot star (10000 K): Peak at 290 nm (ultraviolet)

Stefan-Boltzmann Law

The total power radiated by a blackbody is proportional to the fourth power of temperature:

P = \sigma A T^4

Where KaTeX can only parse string typed expression W·m⁻²·K⁻⁴ is the Stefan-Boltzmann constant.

Key Observations

Shape: All curves have the same characteristic shape, peaking at one wavelength
Peak shift: Higher temperatures shift the peak to shorter wavelengths (bluer light)
Total area: Higher temperatures produce much more total radiation (T⁴ dependence)
Color temperature: The peak wavelength determines the apparent color of hot objects
Quantum nature: The curves can only be explained by quantum mechanics, not classical physics

Applications

Astrophysics

Determining stellar temperatures from their spectra
Understanding stellar evolution and classification
Cosmic microwave background radiation analysis

Technology

Thermal imaging and infrared cameras
Incandescent lighting design
Solar energy optimization
Temperature measurement (pyrometry)

Climate Science

Earth's energy balance calculations
Greenhouse effect modeling
Atmospheric radiation studies

Historical Significance

The study of blackbody radiation curves led to several revolutionary discoveries:

Quantum theory birth (1900): Planck's solution to the ultraviolet catastrophe
Energy quantization: Introduction of the concept that energy comes in discrete packets
Foundation for quantum mechanics: Paved the way for Einstein's photoelectric effect and Bohr's atomic model
Modern physics: Bridged classical and quantum physics