Spectrophotometry: Absorption and Scattering

Absorption and Scattering

• Absorption coefficient is a key factor in spectrophotometry.

• The absorption cross-section defines the likelihood of a transition between states.

• The absorption cross-section is the ratio of power absorbed by a molecule to the incident power per unit area.

• The absorption cross-section has units of area.

• Absorption coefficient is also represented as an area.

• The molar absorption coefficient measures the sum of the absorption cross-sections of all the molecules in one mole of a substance.

• The molar absorption coefficient relates to the Avogadro constant NA = 6.022×10⁻²³

• Absorption coefficient as a probability is the probability that a photon will be absorbed while traveling a distance, represented by µₐδz.

• Beer's Law: Φ = Φ₀ exp(-µₐz)

• Spectrophotometry measures optical absorption spectra.

• The detected light intensity can be expressed as Iₗ(λ) = I₀(λ) exp(-µₐ(λ)d)

• µₐ(λ) = -1/d ln(Iₗ(λ)/I₀(λ))

• α(λ) = -1/Cd ln(Iₗ(λ)/I₀(λ))

• A = -log₁₀(Iₗ/I₀) = - log₁₀(exp(-aCd)) = log₁₀(e) aCd.

• T = Iₗ/I₀, A = -log₁₀(T) = eCd

• (Extinction Coefficient) e

• Spectroscopic Inversion is a technique used to estimate concentrations of constituent by measuring multiple wavelengths.

• Sample containing several known chromophores allows estimations of constituent concentrations using measurements from multiple wavelengths.

• A(λ₁) = eₐ(λ₁)Cₐd + e(λ₁)C₈d + eₕ(λ₁)Cₕd

• A(λ₂) = eₐ(λ₂)Cₐd + e(λ₂)C₈d + eₕ(λ₂)Cₕd

• A(λ₃) = eₐ(λ₃)Cₐd + e(λ₃)C₈d + eₕ(λ₃)Cₕd

Optical Scattering

• Scattering in biological tissues is often a dominant characteristic, making them opaque.
• Photon scattering is divided into elastic and inelastic types.
• Elastic scattering conserves energy, and the scattered light has the same frequency as the incident light.
• Inelastic scattering involves energy gain or loss, resulting in scattered light with a different frequency compared to the incident light.
• Elastic scattering is more substantial in most biological tissues at visible and near-infrared (NIR) wavelengths.
• The frequency not exciting any resonance will cause the oscillating dipole to radiate an EM wave.
• A photon with equal energy will be re-radiated in a random direction.
• Light travels at speed c in a vacuum.

Refractive Index

• Light travels at c/v through a medium with a refractive index.
• The emergent wave moves through the medium at c/n speed.
• The apparent change in speed causes refraction, bending the light as it enters a medium with a different refractive index.
• Refractive indices vary spatially, resulting in microscopic and macroscopic scattering.
• The key factor determining whether a refractive index fluctuation will scatter strongly is the relationship between the scatterer's size and the light's wavelength.
• The reduced scattering coefficient incorporates scattering coefficient and anisotropy: µs' = µs(1 - g) [cm⁻¹]
• The mean free path is the average distance a moving particle (like an atom, molecule, or photon) travels between impacts.
• The purpose of µs' is to describe photon diffusion in a random walk with a step size of 1/µs' [cm], where each step incorporates isotropic scattering.
• g = <cos θ>

Explore the principles of absorption and scattering in spectrophotometry. This quiz covers important concepts such as the absorption coefficient, Beer's Law, and the relationship between molar absorption coefficients and Avogadro's constant. Test your knowledge of how light interacts with matter and the mathematical expressions involved.