Biological Techniques: Photometry and X-Ray Diffraction Study Guide

Photometry (Optical Methods of Analysis)

Definition: Photometry refers to spectroscopic techniques based on the measurement of absorption or emission of electromagnetic radiation, specifically in the ultraviolet (UV), visible, and infrared (IR) regions.
Core Principle: It involves measuring light intensity. In a given sample, atoms or molecules must absorb or emit light radiation when exposed to specific conditions.
Spectroscopic Basis: Analysis involves measuring the intensity and wavelength of radiation that is either absorbed or transmitted. This provides a sensitive foundation for detection and quantitation.

Types of Optical Methods of Analysis

Colorimetry: Involves measuring the absorption of light radiation by a colored solution.
Spectrophotometry: Measures the absorption of light within a narrow wavelength band by molecules in solution.
Atomic Absorption Analysis: Measures the absorption of light radiation by free atomic species.
Atomic Emission Analysis: Based on the emission of light by atoms in an excited electronic state.
Fluorimetry: Involves estimating the amount of a fluorescent substance within a given sample.

Molecular Absorption Analysis

Concentration Principle: The absorption of light by a compound in solution increases relative to the concentration of the compound. This effect is exploited in both colorimetry and spectrophotometry.
Direct vs. Indirect Estimation: Colored compounds can be estimated directly. Compounds that are not inherently colored but produce colored derivatives when reacted with specific chemical reagents can also be analyzed.

The Laws of Absorption (Beer-Lambert's Law)

The absorption of light radiation by solutions is elucidated by combining two laws: Beer’s Law and Lambert’s Law. These relate absorption to concentration and the thickness of the absorbing layer.
Beer’s Law: * This law states that the absorption of light is directly proportional to the number of absorbing molecules. * Transmittance decreases exponentially as the concentration of absorbing molecules increases. * Mathematical Expression: $\log_{10} \frac{I_O}{I} \propto C$ or $\log_{10} \frac{I_O}{I} = \varepsilon C$ * Where $\log_{10} \frac{I_O}{I}$ is the Absorbance ( $A$ ), $C$ is the concentration, $\varepsilon$ is the molar extinction coefficient (or molar absorptivity), $I_O$ is the incident light, and $I$ is the transmitted light.
Lambert’s Law: * This law states that the same proportion of incident light is absorbed per unit thickness regardless of intensity, and each successive unit layer absorbs the same proportion of light falling upon it. * Mathematical Expression: $\log_{10} \frac{I_O}{I} \propto l$ or $\log_{10} \frac{I_O}{I} = kl$ * Where $A = \log_{10} \frac{I_O}{I} = kl$ , $k$ is a constant, and $l$ is the path length.
Combined Beer-Lambert’s Law: * Formula: $A = \log_{10} \frac{I_O}{I} = \varepsilon C l$ * Molar Extinction Coefficient (\varepsilon): A constant numerically equal to the absorbance of a molar solution in a cell with a path length of $1\,\text{cm}$ .
Limitations and Calibration: * Lambert’s law holds in all cases, but Beer’s law is only obeyed by dilute solutions. * In higher concentrations, the association of absorbing molecules can occur, causing a "tailing off" in light absorption. * Estimation of unknowns must be performed within the concentration range where Beer’s law is valid. * Standard Curve: It is standard practice to plot a graph of absorbance against concentration to determine the valid range where Beer’s law is obeyed.

Absorbance and Transmittance

Absorbance (A): A measure of the fraction of light radiation absorbed by a sample solution.
Transmittance (T): The fraction of incident light that is not absorbed (i.e., it is transmitted through the solution).
Inverse Relationship: As the absorbance of a solution increases, the transmittance decreases.

Colorimetry

Definition: A photometric method measuring the absorption of visible light radiation by a colored solution.
Instrumentation (Colorimeter): * Light source: Tungsten lamp. * Monochromator: Filter. * Slit: Governs light entry. * Optical cell / Cuvette: Holds the sample (typically glass). * Photoelectric cell: The detector. * Galvanometer: Displays the reading.
Mode of Operation: 1. White light from the tungsten lamp passes through a condenser lens to create a parallel beam. 2. This beam hits a filter that selects a specific wavelength of radiation. 3. The light passes through the glass cuvette containing the solution. 4. Some light is absorbed; the transmitted light is detected by the photoelectric cell. 5. The meter is first adjusted to $100\%$ \ transmittance (zero absorbance) using a blank solution. 6. The sample replaces the blank, and absorbance is read directly. 7. Concentration is determined using a standard/calibration graph.
Applications of Colorimeter: 1. Printing industries: Evaluating quality of ink and paper. 2. Food and food processing industries. 3. Clinical laboratories/hospitals: Determining biochemical composition of blood, urine, cerebral spinal fluid (CSF), plasma, and serum. 4. textile and paint industries. 5. Gemology: Examining visual characteristics of diamonds and precious stones. 6. Cosmetology: Measuring UV protection levels in skin-care products. 7. Water purity: Screening for chemicals like cyanide, iron, fluorine, chlorine, and molybdenum. 8. Electronics: Evaluating color contrast and brightness on mobile, computer, and TV screens. 9. Pharmaceuticals: Identifying inferior/counterfeit goods and medications. 10. Hematology: Determining hemoglobin levels in blood samples.
Advantages: * Quick and affordable evaluation. * Simple quantitative analysis of colored chemicals. * Results available in less than a second. * Portable colorimeters can perform $100$ to $300$ measurements using four AA batteries.
Disadvantages: * Analyzing colorless substances is laborious (requires derivation). * Visible range only ( $400\,\text{nm}$ to $700\,\text{nm}$ ); does not work in UV or IR spectra. * Requires setting a spectrum range rather than a specific discrete wavelength. * Difficulty measuring on light-reflecting surfaces.

Spectrophotometry

Definition: A method measuring the absorption of narrow wavelength bands of radiation by molecules in solution. The instrument used is the spectrometer or spectrophotometer.
History: Invented in $1940$ by Arnold J. Beckman and colleagues at the National Technologies Laboratory (NTL), known as the Beckman DU spectrophotometer.
Essential Components: * Stable radiant energy source. * System of lenses, mirrors, and slits to parallelize and focus light. * Monochromator to resolve radiation into individual wavelengths. * Cuvette (sample holder). * Radiation detector and readout system (meter or recorder).
Radiation Sources: * UV Radiation: Hydrogen and deuterium lamps ( $180\,\text{nm}$ to $350\,\text{nm}$ ). These use electrodes in a glass tube with a quartz window. * Visible/Near IR: Tungsten filament lamp ( $350\,\text{nm}$ to $2500\,\text{nm}$ ). * Other: Xenon lamp.
Monochromator: A device using lenses to resolve polychromatic radiation into narrow, individual wavelengths (monochromatic radiation).
Detectors: * Photoelectric detectors: For UV and visible light. * Thermocouple: For middle and far infrared radiation. * Photoconductivity cell: For near-infrared radiation. * Photomultiplier tube: For detecting light passing through sample solutions (standard in many spectrophotometers).
Differences from Colorimeter: * Spectrophotometers can discriminate between compounds with overlapping spectra. * Uses prisms instead of filters. * Uses photomultiplier tubes instead of simple photocells. * Operates in both UV and visible regions, whereas colorimeters are limited to visible light. * Offers improved resolution, sensitivity, and versatility.
Applications: 1. Detecting substance concentration. 2. Identifying impurities. 3. Structure elucidation of organic compounds. 4. Monitoring dissolved oxygen in freshwater and marine ecosystems. 5. Characterization of proteins. 6. Detecting functional groups. 7. Hospital respiratory gas analysis. 8. Determining molecular weight. 9. Identifying classes of compounds in pure states or biological preparations.

X-Ray Diffraction (XRD)

Introduction to X-Rays: High penetration electromagnetic radiation with wave properties allowing for diffraction.
Diffraction Process: Occurs when a wave meets a barrier with openings roughly the same size as the wavelength. In crystals, the spacing between atoms/ions is in the correct range to act as a diffraction grating for X-rays.
Basic Concept: X-ray wavelengths are comparable to the atomic spacing in crystals. When passing through, they spread/bend to form interference patterns. These patterns reveal the geometric structure and properties of crystals.
Electron Interaction: Atoms produce diffraction patterns because their electron clouds interact with the X-ray's electric field. * Large Atoms: Have many electrons and produce the strongest diffraction patterns. * Small Atoms (e.g., Hydrogen): Have little effect on X-rays due to few electrons.
Measurement: A diffractometer is used for accurate intensity measurement. Computerization allows for the production of electron density maps.
Bragg’s Law: * Introduced by Sir W.H. Bragg and Sir W.L. Bragg. * Statement: When X-rays are incident on a crystal surface at angle $\theta$ , they reflect at the same angle $\theta$ . Constructive interference occurs when the path difference is equal to a whole number ( $n$ ) of wavelengths. * Formula: $n \lambda = 2d \sin(\theta)$ * Where $n$ is an integer, $\lambda$ is the wavelength, $d$ is the distance between atomic planes, and $\theta$ is the angle of incidence.
XRD Applications: * Discovering 3D structures of matter, atoms, or molecules. * Primary tool in crystallography. * Determining electron arrangements to deduce molecular shapes. * Determining structures of simple molecules (amino acids, sugars, nucleic acid components) and complex molecules (proteins, enzymes). * Historical Milestone: Led to the discovery of the double helical structure of DNA.