A typical lightbulb contains a tungsten filament that...

A typical lightbulb contains a tungsten filament that reaches a temperature of about $2850 \mathrm{K}$, roughly half the surface temperature of the Sun. (a) Treating the filament as a blackbody, determine the frequency for which its radiation is a maximum. (b) Do you expect the lightbulb to radiate more energy in the visible or in the infrared part of the spectrum? Explain.

A typical lightbulb contains a tungsten filament that reaches a temperature of about $2850 \mathrm{K}$, roughly half the surface temperature of the Sun. (a) Treating the filament as a blackbody, determine the frequency for which its radiation is a maximum.
(b) Do you expect the lightbulb to radiate more energy in the visible or in the infrared part of the spectrum? Explain.

Key Concepts

Wien's Displacement Law

Wien’s displacement law provides the relationship between the temperature of a blackbody and the wavelength or frequency at which its emitted radiation is maximized. For temperature T, the law indicates that the peak wavelength is inversely proportional to T, and when expressed in frequency terms, the peak frequency is directly proportional to the temperature. This law is fundamental when predicting the most intense part of the emission spectrum for objects like tungsten filaments.

Blackbody Radiation

Blackbody radiation refers to the theoretical model of an object that absorbs all incident electromagnetic radiation and re-emits energy solely based on its temperature. This model simplifies the analysis of radiation characteristics and serves as a benchmark for understanding real-life emitters such as lightbulb filaments. The blackbody concept allows calculations of spectral energy distributions and peak emission using temperature-dependent laws.

Electromagnetic Spectrum

The electromagnetic spectrum is the range of all types of electromagnetic radiation, including infrared, visible, ultraviolet, and beyond. Understanding the distribution of energy across different parts of this spectrum helps in determining which range, such as visible or infrared, dominates the emission from objects at a given temperature. In the context of lightbulbs, this concept explains whether the majority of the emitted energy falls within the visible or infrared regions.

Spectral Energy Distribution

The spectral energy distribution describes how the intensity of radiation emitted from a blackbody or any physical body varies with frequency or wavelength. This distribution is important when analyzing how energy is apportioned across the different spectrum regions, and it is directly influenced by the temperature of the emitter. The shape and peak of this distribution, which are derived using Wien's displacement law, help in understanding the relative amounts of visible versus infrared radiation emitted.

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