A tungsten filament of a glowing lightbulb has a temperature...

A tungsten filament of a glowing lightbulb has a temperature of approximately $2000 \mathrm{~K}$. (a) Assuming the operating filament is a blackbody, determine the peak wavelength of its emitted radiation at this temperature. (b) Why does your answer to part (a) suggest that more energy from a lightbulb goes into heat than into light?

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Key Concepts

Electromagnetic Spectrum (Infrared vs. Visible Light)

The electromagnetic spectrum comprises various types of radiation including infrared and visible light. Understanding where the peak emission falls on this spectrum is crucial, as it reveals whether an object primarily emits energy in forms that are visible to the human eye or as heat (infrared radiation). In cases where the peak is in the infrared region, it indicates that more energy is released as heat rather than visible light.

Wien's Displacement Law

Wien's displacement law establishes a relationship between the temperature of a blackbody and the wavelength at which its emission spectrum peaks. It states that the peak wavelength is inversely proportional to temperature, meaning that higher temperatures shift the peak emission towards shorter wavelengths. This law is essential for determining the dominant type of radiation emitted by objects at given temperatures.

Blackbody Radiation

Blackbody radiation refers to the theoretical model in which an object absorbs and re-emits all incident electromagnetic energy. This concept is fundamental in understanding how temperature governs the spectrum of radiation emitted by the object, allowing us to predict the energy distribution across different wavelengths.

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