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Chapter 12: Problem 1

Under daylight conditions, the human eye exhibits maximum sensitivity to light at a wavelength of \(555 \mathrm{~nm}\). At what temperature (K) would a blackbody emit light with a peak intensity at this wavelength?

Short Answer

Expert verified
Answer: The temperature of a blackbody that emits light with a peak intensity at a wavelength of 555 nm is approximately 5210 K.

Step by step solution

01

Convert the given wavelength to meters

The wavelength is given in nanometers, we need to convert it to meters to use in Wien's Law: $$\lambda_{max}=555\mathrm{~nm}\times\frac{1~\mathrm{m}}{10^9~\mathrm{nm}}=5.55\times10^{-7}\mathrm{~m}$$
02

Rearrange Wien's Law formula to isolate the temperature (T)

To find the temperature, we need to rearrange the Wien's Law formula to get T on one side: $$T=\frac{b}{\lambda_{max}}$$
03

Substitute the values into the formula

Now we can substitute the values of \(\lambda_{max}\) and b into the formula to find the temperature: $$T=\frac{2.898\times10^{-3}~\mathrm{m\cdot K}}{5.55\times10^{-7}~\mathrm{m}}$$
04

Calculate the temperature

Divide the values to find the temperature of the blackbody: $$T\approx\frac{2.898\times10^{-3}}{5.55\times10^{-7}}\approx5214.41~\mathrm{K}$$
05

Round off the answer

Round off the answer to a reasonable number of significant digits. In this case, round it to 3 significant digits: $$T\approx5210~\mathrm{K}$$ The temperature of a blackbody that emits light with a peak intensity at a wavelength of \(555 \mathrm{~nm}\) is approximately \(5210~\mathrm{K}\).

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Most popular questions from this chapter

Imagine the Earth is on the surface of a sphere whose radius is equal to the sun-Earth distance, \(1.50 \times 1011 \mathrm{~m}\). If the total radiant flux from the sun (W) calculated above is evenly distributed over the surface of that imaginary sphere, what is the average flux in \(\mathrm{W} \mathrm{m}^{-2}\) ?
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