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Thermal Radiation. Quantum Nature of Light.

Problem 5.260

An isotropic point source emits light with wavelength λ=589nm.\lambda=589 \mathrm{nm} . The radiation power of the source is P=10 WP=10 \mathrm{~W}. Find: (a) the mean density of the flow of photons at a distance rr =2.0 m=2.0 \mathrm{~m} from the source: (b) the distance between the source and the point at which the mean concentration of photons is equal to n=100 cm−3n=100 \mathrm{~cm}^{-3}.

Reveal Answer
5.260. (a) ⟨j⟩=Pλ/8π2cℏr2=6⋅1013 cm−2 s−1\langle j\rangle=P \lambda / 8 \pi^{2} c \hbar r^{2}=6 \cdot 10^{13} \mathrm{~cm}^{-2} \mathrm{~s}^{-1} (b) r=Pλ/2ℏn/2πc=9 mr=\sqrt{P \lambda / 2 \hbar n} / 2 \pi c=9 \mathrm{~m}
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