 = (4/3ħc) n em2  (Nm-Nn) (o-) 1 2 3 4 Square of the transition moment n em2 Frequency of the light  Population difference (Nm- Nn) Resonance factor - Dirac delta function (0) = 1

 = (4/3ħc) n em2  (Nm-Nn) (o-) 1 2 3 4 (Nm- Nn)

I = Ioe-γl Beer’s Law

I = Ioe-γl

I = Ioe-γl  = (4/3ħc) n em2  (Nm-Nn) (o-) 1 2 3 4 1 2 3 4 Three Cases

I = Ioe-γl  = (4/3ħc) n em2  (Nm-Nn) (o-) 1 2 3 4 1 2 3 4 Three Cases Nm > Nn

I = Ioe-γl  = (4/3ħc) n em2  (Nm-Nn) (o-) 1 2 3 4 1 2 3 4 Three Cases Nm > Nn  +ve

I = Ioe-γl  = (4/3ħc) n em2  (Nm-Nn) (o-) 1 2 3 4 1 2 3 4 Three Cases Nm > Nn  +ve I < Io Absorption

I = Ioe-γl  = (4/3ħc) n em2  (Nm-Nn) (o-) 1 2 3 4 1 2 3 4 Three Cases Nm > Nn  +ve I < Io Absorption Nm = Nn

I = Ioe-γl  = (4/3ħc) n em2  (Nm-Nn) (o-) 1 2 3 4 1 2 3 4 Three Cases Nm > Nn  +ve I < Io Absorption Nm = Nn  = 0

I = Ioe-γl  = (4/3ħc) n em2  (Nm-Nn) (o-) 1 2 3 4 1 2 3 4 Three Cases Nm > Nn  +ve I < Io Absorption Nm = Nn  = 0 I = Io Saturation

I = Ioe-γl  = (4/3ħc) n em2  (Nm-Nn) (o-) 1 2 3 4 1 2 3 4 Three Cases Nm > Nn  +ve I < Io Absorption Nm = Nn  = 0 I = Io Saturation Nm < Nn

I = Ioe-γl  = (4/3ħc) n em2  (Nm-Nn) (o-) 1 2 3 4 1 2 3 4 Three Cases Nm > Nn  +ve I < Io Absorption Nm = Nn  = 0 I = Io Saturation Nm < Nn  -ve

I = Ioe-γl  = (4/3ħc) n em2  (Nm-Nn) (o-) 1 2 3 4 1 2 3 4 Three Cases Nm > Nn  +ve I < Io Absorption Nm = Nn  = 0 I = Io Saturation Nm < Nn  -ve I > Io Stimulated Emission

The maser may switch of after say 3 days so the dimension of the cloud can be estimated from the time for the light wave to pass through the cloud as about 1/100th of a ly and leave the molecules in their lower states. It will take several days to pump up to population inversion again and switch on again Harry Kroto 2004