University Context

The content originates from Al-Khwarizmi College of Engineering at the University of Baghdad, specifically within the Biomedical Engineering Department. Assistant Lecturer Alaa Aldoori authored this document as part of the curriculum for the 4th stage of the 2025-2026 academic year, focusing on Laboratory Instrumentation, with a particular emphasis on Beer-Lambert Law, Colorimetry, and Spectrophotometry.

Colorimeter

A photoelectric colorimeter is an analytical device designed to measure the transmittance and absorbance of light as it passes through a liquid sample.
The colorimeter assesses either the intensity or concentration of the color produced when a specific reagent interacts with the liquid sample. Notably, the color can either be an inherent characteristic of the solution or induced through the addition of other reagents.

Interaction of Radiation with Matter

When a beam of radiant energy encounters a substance's surface, it interacts with the atoms and molecules present. This interaction can yield several outcomes, including:

1. Refraction: A notable change in the light's direction occurs as it transitions between media of differing densities.
2. Reflection: The beam redirects back to its source, akin to a mirror effect.
3. Absorption: Certain components of the light spectrum are retained within the substance.
4. Transmission: Portions of the light manage to pass through the medium without alteration.

It is crucial to note that this interaction does not result in a permanent energy transfer, and the speed of radiation in a medium is lower than that in a vacuum, influenced by the concentration and type of constituents present in the medium.

Laws Relating to Absorption of Radiation

Lambert's Law

Lambert's Law is concerned with the relationship between light transmission and the thickness of an absorbing medium. It posits that as a monochromatic light beam traverses a colored solution, its intensity decreases in proportion to the thickness of the solution. Importantly, the amount of light absorbed remains consistent, independent of the incident light's intensity, assuming no other changes in the medium occur.

Mathematical Formulation of Lambert's Law

The equation can be represented as follows:

• Let:
  • $T = ext{Transmittance}$
  • $I_0 = ext{Intensity of the incident light at wavelength } \lambda$
  • $I = ext{Intensity of the transmitted light}$
  • $b = ext{Thickness of the medium}$
  • $k = ext{Absorptivity of the sample}$

Beer’s Law

Beer’s Law relates to how transmitted light intensity diminishes as it passes through a colored solution in relation to its concentration. Higher concentrations lead to lower transmitted intensity.

Mathematical Formulation of Beer’s Law

The equation is essentially similar to Lambert’s Law, taking into consideration concentration:

• Let:
  • $c = ext{Concentration}$
  • $T = ext{Transmittance}$
  • $I_0 = ext{Intensity of the incident light at wavelength } \lambda$
  • $I = ext{Intensity of the transmitted light}$
  • $k = ext{Absorptivity of the sample}$

Combining Lambert's and Beer's Laws leads to the famous Beer-Lambert Law:

Beer-Lambert Law

$A = abc$
Where:

• $A = ext{Absorbance}$
• $a = ext{Absorption coefficient}$
• $b = ext{Thickness of the medium (cm)}$
• $c = ext{Concentration (g/l or mol/l)}$

If molarity is utilized, the absorption coefficient ($ε$) becomes the molar absorption coefficient:

$A = ext{ε}bc$

Exponential Form of Beer-Lambert Law

The Beer-Lambert Law can also be expressed in the exponential format as:

$T = \frac{I}{I_0}$
Where:

• $T$ indicates transmittance.
• The percentage transmittance can be calculated as:

ext{%T} = \frac{I}{I_0} imes 100 = 100T

Types of Colorimeters

Colorimetric analysis generally emphasizes measurements in the visible region of the electromagnetic spectrum (400–700 nm) and may extend into the ultraviolet range. The sample compartment is structured to accommodate cuvettes with liquid samples for analysis. Common types of colorimeters include:

1. Single Beam Filter Photometers
2. Double Beam Filter Photometers
3. Probe-Type Photometers
4. Multi-channel Photometers
5. Portable Colorimeters

The operational procedure often comprises first measuring a reference sample followed by analysis of the sample itself.

Spectrophotometer

A spectrophotometer serves as a sophisticated version of the colorimeter, facilitating qualitative and quantitative measurements of analytes in a solution. Its key components include:

1. Light Source: Emitting suitable intensity of light for measurement.
2. Collimator: Aligns light into a narrow beam.
3. Monochromator: Isolates specific wavelengths of light.
4. Cuvette: Holds the liquid sample for measurement.
5. Photoelectric Detector: Converts light signal into an electrical signal.
6. Digital Display: Provides visual output of the measurements.

Radiation Sources in Spectrophotometry

1. Tungsten Lamp: Predominantly used for visible light measurements.

   • Reliable and affordable with a major portion of output in the near-infrared range (15-20% in the visible range). Note that ongoing vaporization can alter its spectral properties.
   • Tungsten-Halogen variant: Provides continuous spectrum from 360–950 nm, particularly efficient in the 320–380 nm range.

2. Deuterium Lamp: Utilized for ultraviolet measurements, recognized for high intensity over 190–380 nm. These lamps typically exceed 500 hours of operational lifespan and require specific envelopes for UV transmission.

Wavelength Selectors

These include filters and monochromators that isolate the required wavelength from the light source. Filters can be:

1. Glass Filters: Using colored media but tend to have wide spectral bandwidths (40-50 nm).
2. Interference Filters: Comprising semi-transparent layers that achieve narrow wavelength isolations (10-15 nm).

Monochromators

Monochromators enhance wavelength isolation better than filters through optical systems like prisms and diffraction gratings, allowing precise analysis typically over 220 to 950 nm with bandwidths down to 0.5 nm.

Photometric Systems

Photodetectors are key to converting light energy into electrical signals, with common types including:

1. Photomultiplier Tubes: Operate based on the photoelectric effect and achieve high sensitivity.
2. Silicon Photodiodes: Based on changes in electrical properties due to light exposure; notable for their cost-effectiveness.

Sample Holders

Types of sample holders include:

1. Rectangular Liquid Cells
2. Cylindrical Liquid Cells
3. Microcells
4. Quartz or Fused Silica Cells
5. Silica Glass Cells
6. Plastic Cells

Microprocessor-Based Spectrophotometers

Modern systems leverage microprocessors for automation of operational functions, including:

• Wavelength scanning
• Light source selection
• Baseline correction and signal processing
• Data interface through keyboards with displays capable of reporting results.

References

1. Compendium of Biomedical Instrumentation Volume 1 - Raghbir Singh Khandpur
2. Handbook of Second Edition Biomedical Instrumentation - Raghbir Singh Khandpur
3. Wheeler, Lawrence A. "Clinical laboratory instrumentation." Medical instrumentation: application and design. (1998)