Past exam of the chemistry course of the year 1 of the natural sciences course of the University of Cambridge / 2024 / Paper 1 / 4 / a / i / Solution

The decadic Beer-Lambert law can be writtenHere $l$ is the path length in metres, $c$ is concentration in $\mathrm{mol}{\mathrm{L}}^{-1}$ or M, and $\epsilon$ is the decadic molar attenuation coefficient in ${\mathrm{M}}^{-1}{\mathrm{m}}^{-1}$. The intensity ratio and the exponent are dimensionless. Equivalently $I=I_0{e}^{-\kappa lc}$ with $\kappa =(\ln 10)\epsilon$ in the same units. Defining the logarithm convention avoids a missing factor of $\ln 10$.