Principles of Spectrometry and Light-Matter Interaction
Introduction to Spectrometry
Frequency: The frequency of light is a fundamental property in spectrometry.
Color: The color of light is determined by its wavelength, which is crucial for understanding absorption.
Spectrometry Fundamentals
Spectrometry involves the measurement of the quantity of energy transmitted through a sample. This radiant energy is typically monochromatic radiation of a single wavelength, or for practical reasons, a very narrow band of wavelengths. The measurement of the transmitted radiation is performed by highly sensitive equipment such as photocells, photomultiplier tubes, and thermopiles.
Interaction Between Radiant Energy and Matter
Atoms, ions, or molecules can absorb radiation if the photon’s energy matches the natural frequency of vibration of their electrons. Different energy photons produce different effects on the absorbing material:
Nuclear Transformations
Very short wavelengths, for example, gamma rays, can cause nuclear transformations, leading to the emission of high-energy electrons.
Inner Electron Excitation
X-ray absorption produces the excitation or transmission of electrons in the inner layers of the atom. This process is largely independent of the physical state or chemical combination of the atoms.
Outer Electron Excitation
The absorption of radiation in the ultraviolet and visible parts of the spectrum primarily affects outer shell electrons, causing electronic transitions.
Molecular Vibrations and Rotations
Infrared radiation alters the vibrations of molecules. Absorption of energy in the far-infrared and microwave regions causes rotational alterations, which typically require low power.
Absorption Spectrophotometry
Key Definitions in Absorption Spectrophotometry
Understanding the following terms is essential for absorption spectrophotometry:
1. Absorbance (A)
Absorbance is the logarithm (base 10) of the reciprocal of the transmittance (T). It is measured relative to a pure material or solvent reference.
A = log(1/T)2. Absorptivity (a)
Absorptivity is a proportionality constant in Beer’s Law. It relates absorbance to the optical path length (b) and concentration (c) when concentration is expressed in units other than moles per liter.
A = abc3. Molar Absorptivity (ε)
Molar absorptivity is a specific type of absorptivity where the concentration (c) is expressed in moles per liter and the light path (b) in centimeters. It is a characteristic property of a substance at a given wavelength.
A = εbc4. Radiant Power (P)
Radiant power refers to the rate at which radiant energy is transported by a beam of light. It is measured by detectors such as photocells and thermocouples.
5. Transmittance (T)
Transmittance is the ratio of the radiant power transmitted (P) through a sample to the radiant power incident (P₀) on the sample. Both are measured at the same spectral position with the same slit width.
T = P / P₀It is assumed that the incident radiation is parallel and strikes the flat surface of the sample perpendicularly.
Fundamental Laws of Spectrometry
Bouguer’s Law (Lambert’s Law)
This law has two parts:
Constant Proportion of Transmission
For monochromatic radiant energy transmitted through an isotropic, homogeneous medium, the proportion of radiant energy transmitted (T = P/P₀) is a constant, regardless of the incident power.
Geometrical Decrease
The transmitted radiant energy decreases in geometrical progression when the optical path length increases in arithmetic progression.
Mathematically, this can be expressed as:
A = ab or log(1/T) = ab
Where:
- T: Transmittance
- b: Optical path length
- a: Absorptivity of the medium
As the optical path length increases, transmittance decreases, and absorbance increases.
Beer’s Law
Beer’s Law expresses the relationship between transmittance and the concentration of the absorbing material. It states that transmittance decreases exponentially as the concentration of the absorbing substance increases.
Mathematically, this can be expressed as:
A = ac or A = -log(T) = log(P₀/P) = log(1/T)
Where:
- A: Absorbance
- a: Absorptivity
- c: Concentration
The Beer-Lambert Law (Combined Law)
The fundamental laws of spectrometry are combined into the Beer-Lambert Law. This law indicates that the graphic representation of absorbance as a function of concentration, at a constant optical path length, is a straight line with a slope equal to the product of the absorptivity and the optical path length.
In this relationship, the absorptivity of the substance has dimensions related to units of concentration and optical path length.