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I was told by my supervisor that there is a relation between these two and he talked about a coefficient connecting the two of them. I am currently brushing up a lot of chemistry as I'm a physics student currently working on an internship mainly working with physical chemistry.

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A plane wave moving along $z$ has intensity $I$ that decreases as

$$dI=-\alpha Idz$$

which yields Beer's law

$$I=I_oe^{-\alpha z}$$

where $\alpha$ is the absorption coefficient in cm$^{-1}$, at frequency $\omega$, for a transition from state $i$ to $f$, and which depends on the population difference and on the optical cross section $\sigma_{if}$ (cm$^2$) as

$$\alpha_{i,f}=\sigma_{i,f}(N_i-N_f)$$

and, as is almost always the case, $N_f\ll N_i$ then $\alpha_{i,f}=\sigma_{i,f}N_i$. As $N$ is the number density it is common to replace this with concentration (mol/dm$^3$) and then Beer's law becomes

$$I=I_oe^{-\epsilon [C] z}$$

where $\epsilon$ is the extinction coefficient in dm$^3$/mol/cm at a given wavelength.

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