Which mathematical constant is represented by e in Beer's Law?

• A. e
• B. pi
• C. i
• D. 1

Answer: (A)

Beer's Law describes how light intensity decays as it travels through an absorbing solution. That decay is exponential because a small slice of material reduces the current intensity by a proportion, so the change in intensity with distance follows a differential equation. Solving dI/dx = -ε c I gives I = I0 e^{-ε c x}. The e here is Euler’s number, the base of natural logarithms, about 2.71828. This is why the exponential term contains e and can also be written with natural logarithms as ln(I0/I) = ε c l. In other words, e is the fundamental constant that governs continuous exponential decay in Beer's Law. The other constants listed (pi, the imaginary unit i, or 1) don’t appear in the standard Beer's Law expression for absorbance.