Contemporary Challenges 2021
Students use a PhET to explore properties of the Planck distribution.
This activity follows Planck spectral 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
