A metal-complex solution absorbs at 480 nm with molar extinction coefficient 15000 L/(mol cm). Path length is 1.0 cm and transmittance 20.5%. Find concentration in mol/L.
Convert percent transmittance to fraction T = 0.205. Absorbance is $A=-\log_{10}(0.205)=0.68825$. Beer–Lambert gives $c=A/(\epsilon l)=0.68825/(15000\times1)=4.59\times10^{-5}$ mol/L, C. Using 20.5 directly in the logarithm would give an unphysical negative absorbance.
More Spectroscopy: Atomic spectroscopy; Russell-Saunders coupling; Term symbols and spectral details; origin of selection rules. Rotational, Vibrational, Electronic and Raman spectroscopy of diatomic and simple polyatomic molecules. Line broadening and line widths; simple properties of Gaussian and Lorentzian line shapes. Molecular spectroscopy: Absorbance, Beer- Lambert’s law, Einstein’s coefficient, Jablonski diagram. Relationship of transition moment integral with molar extinction coefficient and oscillator strength. Basic principles of Nuclear Magnetic Resonance: Gyromagnetic ratio; Chemical shift, nuclear coupling. questions
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