Lambert's and Beer-Lambert's Law of Radiation

Lambert's Law

• The decrease in intensity of radiation with thickness of the solution is directly proportional to the intensity of the incident light.
• The law is expressed as: 𝑑𝐼/𝑑𝑙 = −𝐾′ 𝐼, where 𝐾′ is the absorption coefficient.
• The extinction coefficient (K) is related to the absorption coefficient (K') by: 𝐾 = 2.303 𝐾′, and its unit is cm-1.
• The absorbance (A) is related to the extinction coefficient (K) and the path length (l) by: A = 𝐾𝑙.

Beer-Lambert's Law

• The decrease in intensity of radiation with thickness of the solution is directly proportional to the intensity of the incident light and the concentration of the solution.
• The law is an extension of Lambert's law, taking into account the concentration of the solution.

Interpreting UV-Visible Spectra

• Non-conjugated alkenes show an intense absorption below 200 nm and are therefore inaccessible to UV spectrophotometers.
• Non-conjugated carbonyl group compounds give a weak absorption band in the 200-300 nm region.
• Conjugation of double bonds in a compound shifts the λmax to longer wavelengths.
• Conjugation of C=C and carbonyl groups shifts the λmax of both groups to longer wavelengths.

Molar Absorption Coefficients

• The molar absorption coefficient (ε) is a measure of the ability of a molecule to absorb radiation at a given wavelength.
• The absorbance (A) of a mixture can be calculated using the molar absorption coefficients of the individual components.

Electronic Transitions

• Electronic transitions involve the promotion of an electron from a electronic ground state to a higher energy state.
• Typical electronic transitions occur from the Highest Occupied Molecular Orbital (HOMO) to the Lowest Unoccupied Molecular Orbital (LUMO).
• σ-orbitals are typically the lowest energy occupied orbitals, while π-orbitals are of somewhat higher energy.
• Anti-bonding orbitals (σ* and π*) are of higher energy than their corresponding bonding orbitals.