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hw_4_solu

# hw_4_solu - Homework4Solutions 1a.=4.051021Joules....

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Homework 4 Solutions 1a. Room temperature corresponds to k T = 4.05 × 10 21 Joules . Photons of this energy would have frequency f = E/h = 6.11 × 10 12 Hz and wavelength λ = c/f = 49.1 microns . Is it reasonable that a hot body starts to glow around 1000°C? Wien’s displacement law tells us that the peak wavelength of a blackbody depends on its temperature: nm 2276 K 1273 K m 10 898 . 2 3 peak = × = = T b λ The peak wavelength is outside the visible range, but there will be a distribution of photon wavelengths emitted. From the calculation here, yes , it’s reasonable that a hot body would just start to have enough photons of sufficiently short wavelength that we could see a reddish glow at this temperature. In fact, if we look this up, we can find the blackbody distribution: (source: http://en.wikipedia.org/wiki/Wien's_displacement_law and http://en.wikipedia.org/wiki/Black_body_spectrum ) The chart shows that objects start to glow around 1000, which is pretty close to 1273 K, so yes, it’s reasonable that a hot body would start to glow around 1000°C.

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1b. flux ൌ ܬ ൌ 1.6 כ 10 ିଵ଴ W ߣ ൌ 560 nm ܧ ൌ ݄݂݊ ൌ ݄݊ܿ ߣ ܧ ൌ ܬݐܣ ୮୳୮୧୪ ൌ ܬݐߨݎ Let’s say the diameter of a pupil is 4 mm (this seems reasonable according to http://en.wikipedia.org/wiki/Pupil ) Solve for n : ݊ ൌ ܬ ݐ ܣ ߣ ݄ ܿ ܬ ݐ ߨ ݎ ߣ ݄ ܿ ݊ ൌ ൬1.6 כ 10 ିଵ଴ joule s m
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