Spectrometric Methods Flashcards

CH 6 An Introduction to Spectrometric Methods

General Properties of Electromagnetic Radiation

Electromagnetic radiation can be depicted as an electromagnetic wave, showing electric and magnetic vectors, amplitude, and wavelength. However, this depiction does not explain particle effects of light such as photons and the photoelectric effect. The diagram also shows a plane-polarized EM wave. In spectrophotometry, the electric vector (absorption) is crucial, while the magnetic wave is used in NMR and is responsible for the absorption of RF waves.

Interaction of Light with Matter

Light interacts with matter through several phenomena:

• Absorption
• Reflection
• Refraction
• Diffraction
• Scattering

Scattering is a predominant interaction where light is scattered from particles with the same energy (wavelength). This type of light scattering is called ELASTIC, also known as Rayleigh Scattering, named after Lord Rayleigh (John William Strutt).

Diffraction of Light

Diffraction of light is a consequence of the interference of light waves, where waves combine to produce a new set of waves.

Wave Characteristics

The relationship between the velocity of light, wavelength, and frequency is given by: c = n \lambda. In a vacuum, the velocity of light c = 2.9979 \times 10^8 m/s. When light passes through matter, the refractive index n is fixed, and the wavelength \lambda changes.

Approximation: c = 3 \times 10^8 m/s = 3 \times 10^{10} cm/s

Units in Spectrometry

• UV-Vis region: nanometers (nm)
• IR region: wavenumber (cm⁻¹)

Example: Determine the wavenumber for the Ar+ laser line at 415.4 nm.

The Electromagnetic Spectrum

The electromagnetic (EM) spectrum encompasses a vast range, necessitating a logarithmic scale. The spectrum includes:

• Gamma ray
• X-ray
• Ultraviolet
• Visible
• Infrared
• Microwave
• Radio

Common Spectroscopic Methods Based on Electromagnetic Radiation

Mathematical Description of a Wave

The magnitude of the electric field at time t is given by: y = A \sin(\omega t + \phi)

Where:

• y = magnitude of electric field at time t
• A = amplitude
• \phi = phase angle
• \omega = angular velocity (\omega = 2\pi\n
  The equation can also be written as: y = A \sin(2\pi t + \phi)
  Waves can be superimposed or added together, leading to constructive and destructive interference.

Addition of Waves

Light waves can be superimposed, resulting in constructive and destructive interference. The addition of waves can be performed mathematically. For a measurement on the resulting wave, the time interval \Delta t must be greater than or equal to the period of one “beat”.

Diffraction Through a Slit

When waves pass through a wide slit, they go through mostly unchanged, with minor diffraction. As the slit narrows, there is more diffraction, making it appear as if the source of the wave is a new source.

Thomas Young's Experiment

In Thomas Young’s experiment, radiation from a single slit hits two closely spaced slits, causing an interference pattern. The angles necessary for maximum constructive interference are observed.

Diffraction Produced by Coherent Radiation

Coherent radiation implies that the two sources have identical frequencies, and the phase relationships between the beams are constant. In practice, a single source is used and passed through two slits.

General Expression for Light Bands

The general expression for the light bands surrounding, and decreasing in intensity, from the central band is given by:

n \lambda = BC \sin \theta

Where:

• n = order of interference
• \theta = angle of diffraction
• BC = distance between the slits

This is a result of coherent light. Using two non-coherent filament light sources results in a blur.

Diffraction Grating

Diffraction gratings are used in modern spectrophotometers to separate wavelengths of light. Constructive interference occurs when:

n \lambda = BC \sin \theta

where n = 1, 2, 3, etc.

Transmission of Radiation

When light passes through a medium other than a vacuum, its velocity changes. This change is quantified by the refractive index of the material:

ni = \frac{c}{nI}

Where:

• c is the velocity of light in a vacuum
• n for liquids is typically 1.3-1.8
• n for solids is typically 1.3-2.5

The interaction of transmission through a medium involves periodic polarization of the atomic and molecular species composing the medium.

Polarization

Polarization refers to the temporary deformation of the electron clouds of the atoms in the medium.

Reflection of Radiation

Reflection occurs at the surface of diffraction gratings. The fraction of reflected radiation increases with increasing differences in refractive index. Whenever there is a change in the refractive index, reflection occurs, leading to losses in the intensity of light.

The fraction of reflected light is given by:

Ir = \frac{(n2 – n1)^2}{(n2 + n1)^2} I0

The Photoelectric Effect

The Photoelectric Effect is the method by which photons of light are converted to an electrical signal and is the basis of the photomultiplier tube. Heinrich Hertz first observed it in 1887, and Albert Einstein explained it in 1905. Millikan experimentally verified Einstein’s work.

Photomultiplier Tube

A photomultiplier tube is a photoemissive device where the absorption of a photon results in the emission of an electron. It amplifies electrons generated by a photocathode exposed to a photon flux. The current flowing from the anode to the ground is directly proportional to the photoelectron flux generated by the photocathode.

Apparatus for Studying the Photoelectric Effect

The surface of the photocathode is coated with an alkali metal or one of its compounds. Monochromatic radiation is directed onto the cathode, which emits electrons if the light is of an energetic wavelength. Applying a voltage V between the cathode and anode results in a current I. The stopping voltage, the voltage that just repels the electron, is used to calculate the kinetic energy of the lowest wavelength light.

Kinetic Energy of Emitted Electron

The kinetic energy (KE) for the lowest emitted electron is given by:

KE = h\nu - w

Where:

• w = work function

Lower wavelength light provides greater KE. By imparting more KE than the work function, the metal will emit an electron in response to the photon.

Interactions of Radiation and Matter

Emission or Chemoluminescence

In atoms, electrons are excited to a higher energy state and then emit a photon as they de-excite.

Absorption

Scattering

Elastic Scattering (Rayleigh Scattering)

Incident radiation hits a particle, and radiation is scattered in all directions at the same wavelength.

Inelastic Scattering (Raman Scattering)

Scattered light loses or gains energy and is scattered at different wavelengths. Electrons are promoted to a virtual state, and as they fall back to a different energy level, energy is lost or gained.

Emitted Light: Continuous Spectra and Line Spectra

Sunlight and light from glowing filaments produce a continuous spectrum. Single atoms, when excited, produce a non-continuous spectrum, where each bright line corresponds to an electronic transition.

Molecular Spectra

Simple molecules can exhibit bands.

Continuum Spectra

This is black body radiation produced by heating a solid to incandescence, such as filament lamps and ceramic IR sources. The position of the spectrum (UV, vis, IR) depends on the temperature of the body; very high temperatures are needed to get UV light.

Absorption of Radiation

Electromagnetic radiation is transferred to the atoms, ions, and molecules of the sample, promoting them from the ground state to a higher energy excited state. Atoms, ions, or molecules have specific discrete energies that they can absorb, corresponding to the energy difference between orbital levels.

Spectrophotometry

Simplest Spectrophotometer

The simplest spectrophotometer is a filter photometer. The filter blocks out all but a small band of light. A variable diaphragm allows the instrument to be set at 0 and 100%T (transmittance). The sample cell is in the path for absorption, and a photoelectric device converts the unabsorbed light for measurement.