This activity follows Planck spectral distribution

Google “phet blackbody spectrum”' and open the simulation.

1. 1. 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.
   2. Check that the peak wavelength decreases with temperature following a \(1/T\) relationship.
2. 1. Use the numerical integration feature (the checkbox labelled “intensity” near the upper-right 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.
   2. Check that these intensities are proportional to \(T^4\). Note, the quick way to check involves ratios: Does \(\frac{I_1}{I_2} = \left(\frac{T_1}{T_2}\right)^4\)?
3. How cold should you make an object if you want zero thermal radiation emitted?
4. (Extra---if your group has time)
   1. 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*}
   2. Estimate the filament surface area \(A\) for a 60 W light bulb.