# Beer-Lambert law

## Main Question or Discussion Point

Hi! I want to ask you something. Why on normal environments the $$\alpha > 0$$ (the coefficient of absorbtion) and in active environments where $N_n > N_m$, where $N_n$(the number of excited atoms) and $N_m$(the number of normal atoms) the coefficient of absorption is $$\alpha < 0$$. I think in normal environments $$\alpha = 0$$. !??

## Answers and Replies

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Hi! I want to ask you something. Why on normal environments the $$\alpha > 0$$ (the coefficient of absorbtion) and in active environments where $N_n > N_m$, where $N_n$(the number of excited atoms) and $N_m$(the number of normal atoms) the coefficient of absorption is $$\alpha < 0$$. I think in normal environments $$\alpha = 0$$. !??
First of all, it's not said in your question, but if we are talking about absorption, stimulated emission, and population of atoms in ground and excited state, we implicitly presume, that the light is passing through a "resonant" enviroment - i.e. the frequency of the light is approximately the same as the frequency of the transition of the atoms from ground to excited state.

This is not the case of what u probably call normal enviroment - e.g. visible light passing through glass. Here the transitions in atoms are in much higher frequencies - for glass somewhere in UV region (300nm) - glass enviroment is subresonant - the absorption in visible light region is negligible.

If you have light passing through a resonant enviroment - laser gain medium (glass doped with some ions) - there are two processes going on inside - absorption and stimulated emission. They happen with same crossections. But if there are more atoms in excited state, it is more likely that the atoms will fall down to the ground state => absorption is negative. If you have enviroment in theormodynamical equilibrium there are always more atoms in ground than in exc. state, and it is more likely, that atoms will be excited => light absorbed.

Hope u'll find it useful.

But isn't in ground states light absorbed and then re-emitted?

malawi_glenn
Homework Helper
the atom de-excitates after a short while, but then the radiation is emitted isotropically.

So in a beam passing through material (like gas), photos will disappear due to aborbtion in atoms. And photons will be emitted into the beam after the atom de-excitates. But that latter number is SO small, due to the isotropical emission of these photons.

That was perhaps not the 100% answer to your question, but it is worth to think about it.

Redbelly98
Staff Emeritus