Contemporary Challenges 2021
Students use a PhET to explore properties of the Planck distribution.
Google “phet blackbody spectrum”' and open the simulation.

 At what wavelength is the peak in spectral intensity
 \(\lambda_{\text{peak}}\) for a black rock on the Earth's surface,
 \(\lambda_{\text{peak}}\) for the black walls of a pizza oven,
 \(\lambda_{\text{peak}}\) for a light bulb,
 \(\lambda_{\text{peak}}\) for the sun.
 Check that the peak wavelength decreases with temperature following a \(1/T\) relationship.

 Use the numerical integration feature (the checkbox labelled “intensity” near the upperright corner of the graph) to find the total intensity, in units of \(\text{W/m}^2\), emitted by
 a black rock on the Earth's surface,
 the black walls of a pizza oven,
 the surface of a tungsten light bulb filament,
 the surface of the sun.
 Check that these intensities are proportional to \(T^4\). Note, the quick way to check involves ratios: Does \(\frac{I_1}{I_2} = \left(\frac{T_1}{T_2}\right)^4\)?
 How cold should you make an object if you want zero thermal radiation emitted?
 (Extraif your group has time)

For an incandescent light bulb with a filament surface area of \(A\), estimate how efficiently it converts electrical energy into visible photons. Hint: you will need to estimate the following ratio:
\begin{align*}
\frac{\text{Electromagnetic radiation in visible wavelengths}}{
\text{Total electromagnetic radiation}
} = \frac{
A\int_{400\text{ nm}}^{700\text{ nm}} S_\lambda(\lambda, T)d\lambda
}{
A\int_{0}^{\infty} S_\lambda(\lambda, T)d\lambda
}
\end{align*}
 Estimate the filament surface area \(A\) for a 60 W light bulb.
 Keywords
 blackbody
 Learning Outcomes
