Blackbody Radiation & Wien's Law

Q: If the absolute temperature of a star is doubled, by what factor does its total power output increase?

16 times According to the Stefan-Boltzmann Law (P propto T^4), doubling the temperature (2T) results in 2^4 = 16 times more power.

Q: A star has a peak wavelength in the infrared part of the spectrum. If its temperature increases significantly, which direction will the peak wavelength shift?

Toward shorter wavelengths (Visible/UV) Wien's Law states lambda_{peak} T = constant. An increase in T requires a decrease in lambda_{peak} to keep the product constant, shifting it toward the blue/UV end of the spectrum.

Explore the Planck radiation spectrum with adjustable temperature. See Wien's displacement law locate the peak wavelength and compare star temperatures from red dwarf to blue giant.

WHAT IS BLACKBODY RADIATION?

A blackbody is an idealized object that absorbs all electromagnetic radiation that falls on it. When heated, it emits radiation in a continuous spectrum that depends only on its temperature. **Wien's Displacement Law** states that the wavelength of peak emission is inversely proportional to the absolute temperature (). This explains why cooler stars look red and hotter stars look blue. The **Stefan-Boltzmann Law** states that the total power radiated is proportional to .

HOW TO USE THIS VISUALIZATION

1. **Adjust Temperature**: Drag the slider to heat or cool the blackbody. Observe how the peak of the intensity curve shifts to shorter wavelengths (left) as temperature increases. 2. **Check Peak Wavelength**: Note the value of and verify Wien's Law calculation. 3. **Compare Spectra**: See where the peak falls relative to the visible light spectrum (red to violet).

CORE FORMULAS

Wien's Displacement Law ($b approx 2.898 imes 10^{-3}$ m K)

Stefan-Boltzmann Law (Total radiated power)

Energy of a photon

AP EXAM CONNECTION

Unit: Unit 7: Quantum, Atomic, and Nuclear Physics (Topic 7.1)
Learning Objective: LO 6.F.1

COMMON MISCONCEPTIONS

Objects must be 'black' in color to be blackbodies (it's a thermal property, not a visual color)
Energy is emitted at only one wavelength (it's a continuous spectrum)

KEY TAKEAWAYS

Hotter objects emit more total radiation.
Hotter objects have shorter peak wavelengths (blue-shifted).
Temperature must be in Kelvin for all radiation laws.
The area under the blackbody curve represents total power radiated.

PRACTICE QUESTIONS

Q1 (QUANTITATIVE): If the absolute temperature of a star is doubled, by what factor does its total power output increase?

Show Answer & Explanation

Answer: 16 times

Explanation: According to the Stefan-Boltzmann Law (), doubling the temperature () results in times more power.

Q2 (CONCEPTUAL): A star has a peak wavelength in the infrared part of the spectrum. If its temperature increases significantly, which direction will the peak wavelength shift?

Show Answer & Explanation

Answer: Toward shorter wavelengths (Visible/UV)

Explanation: Wien's Law states . An increase in requires a decrease in to keep the product constant, shifting it toward the blue/UV end of the spectrum.