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It’s not obvious from Figure how the Planck spectrum
Chapter 7, Problem 38P(choose chapter or problem)
It’s not obvious from Figure 7.19 how the Planck spectrum changes as a function of temperature. To examine the temperature dependence, make a quantitative plot of the function \(u(\epsilon)\) for \(T=3000 \mathrm{~K}\) and \(T=6000 \mathrm{~K}\) (both on the same graph). Label the horizontal axis in electron-volts.
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QUESTION:
It’s not obvious from Figure 7.19 how the Planck spectrum changes as a function of temperature. To examine the temperature dependence, make a quantitative plot of the function \(u(\epsilon)\) for \(T=3000 \mathrm{~K}\) and \(T=6000 \mathrm{~K}\) (both on the same graph). Label the horizontal axis in electron-volts.
ANSWER:
Step 1 of 3
The Planck spectrum of the photons is given by:
\(u(\epsilon)=\frac{8 \pi}{(h c)^{3}} \frac{\epsilon^{3}}{e^{\epsilon / k T}-1}\)
we need to make a plot for this function at temperatures of \(T=3000 \mathrm{~K}\) and \(T=6000 \mathrm{~K}\), the constant in unit of eV are given by:
\(\begin{array}{c} h=4.136 \times 10^{-15} \mathrm{eV} \cdot \mathrm{s} \\ k=8.62 \times 10^{-5} \mathrm{eV} / \mathrm{K} \\ c=3.00 \times 10^{8} \mathrm{~m} / \mathrm{s} \end{array}\)
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