All Problems Thermal Radiation. Quantum Nature of Light.
Problem 5.260
An isotropic point source emits light with wavelength \(\lambda=589 \mathrm{nm} .\) The radiation power of the source is \(P=10 \mathrm{~W}\). Find: (a) the mean density of the flow of photons at a distance \(r\) \(=2.0 \mathrm{~m}\) from the source: (b) the distance between the source and the point at which the mean concentration of photons is equal to \(n=100 \mathrm{~cm}^{-3}\).
5.260. (a) \(\langle j\rangle=P \lambda / 8 \pi^{2} c \hbar r^{2}=6 \cdot 10^{13} \mathrm{~cm}^{-2} \mathrm{~s}^{-1}\) (b) \(r=\sqrt{P \lambda / 2 \hbar n} / 2 \pi c=9 \mathrm{~m}\)