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Therefore, these quantities are related to each other by:

I ν (s) = c u ν (s). (6)

7.6 Spectral Energy Density U ν

The spectral energy density U ν is the volume density of the energy of the
radiation, per unit frequency bandwidth, incoming from all directions (Figure
12).

Figure 12: Spectral energy density: energy of radiation coming from all
directions, contained in a unit volume.

Therefore,
1
I I
U ν = u ν (s)dΩ = I ν (s)dΩ. (7)
c
−1
The unit is J m −3 Hz .

8 Emission and Absorption of Electromag-

netic Radiation

8.1 Elementary Quantum Theory of Radiation (A. Ein-

stein, 1916)
Let us consider a gaseous medium consisting of a large number of particles
(atoms or molecules) of the same species. Let us also consider that each
particle exists in one of the quantum states Z 1 , Z 2 , ..., with energy levels
E 1 , E 2 , ... . If E m < E n for a pair of states Z m and Z n , a particle can
absorb an amount of radiation energy E n − E m in a transition from Z m to
Z n . Also, a particle can emit the same amount of energy in a transition from

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