## Student handout: Blackbody PhET

Contemporary Challenges 2021 (5 years)
Students use a PhET to explore properties of the Planck distribution.

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

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.
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 $\frac{I_1}{I_2} = \left(\frac{T_1}{T_2}\right)^4$?
1. How cold should you make an object if you want zero thermal radiation emitted?
2. (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.

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