<p align="right">Last Update: <font color="#4f81bd">November, 25, 2024</font></p> ## BIG IDEAS - A black body is an idealized object which absorbs all [[Wavelength|wavelengths]] of light and emits its own unique wavelength based on temperature. - The [[Ultraviolet Catastrophe|ultraviolet catastrophe]] is the disconnect between classical theory (intensity changes based on the wavelength) and the experimental results. ### EXAMPLES Coal An iron stove ### Classical Explanation Any object with a temperature above absolute zero emits light at all wavelengths. - Emission is the passing of heat energy. - Reflection is the blocking of incoming thermal radiation and returning it back. Classical physics relies on the formula for intensity ($I$). $I = \frac{2kT}{(\lambda)^2}$ Where $k$ is the Boltzmann’s constant, $T$ is temperature, and $\lambda$ is wavelength in meters. - an increase in T will increase Intensity (energy). - a decrease in $\lambda$ will increase Intensity (energy). ### Predicted vs Actual Results Classical physics predicts a very small wavelength would lead to greater intensity. However, a plot of intensity versus wavelength shows a peak with a drop in intensity at lower wavelengths. The shape of the curve cannot be described by classical physics. ![[Actual vs Predicted Graph.png]] An increase in intensity happens with a temperature increase, and the peak shifts toward the ultraviolet parts of the spectrum. The shift of the peak to ultraviolet led to the name ultraviolet catastrophe. ### Planck's Equation [[Max Planck]] solved the problem of the [[Ultraviolet Catastrophe]] by suggesting radiant energy is emitted in [[Quanta|quantum units]]. $E = nhf = \frac{nhc}{\lambda}$ where - $n$ is a non-negative integer - $f$ is [[Frequency|frequency]] - $h$ is [[Planck’s constant]] ($6.63 x 10^-34 J \cdot s$) - $c$ is the [[Speed of Light|speed of light]] ($3.0 x 10^8 m/s$) - $\lambda$ is [[Wavelength|wavelength]] - In [[Classical Physics|classical physics]] [[Energy|energy]] can have any value. In [[Quantum mechanics|quantum physics]], energy has discrete values. - Quantum energy depends on frequency, not intensity. ### Video <div class="sp-embed-player" data-id="cZVfFMVHCuU"><script src="https://go.screenpal.com/player/appearance/cZVfFMVHCuU"></script><iframe width="100%" height="480" style="border:0;" scrolling="no" src="https://go.screenpal.com/player/cZVfFMVHCuU?width=100%&height=480&ff=1&title=0" allowfullscreen="true"></iframe></div> ### Related Topic --- [[Home|Home]] | [[Quantum mechanics]] | [[Notes Vault/Physics Notes Vault/Quantity of Motion/Quantum Mechanics/Blackbody Radiation|Blackbody Radiation]] | [[Photoelectric Effect]] | [[Atomic Theory]]