Spectroscopic Techniques and Applications Notes

Spectroscopic Techniques and Applications

Spectroscopy is a powerful tool for studying molecular structures and analyzing samples through the interaction of electromagnetic radiation with matter. Electromagnetic radiation is energy transmitted through space at high velocity in a straight line, possessing both electric and magnetic components oscillating in perpendicular planes.

Electromagnetic Radiation

Properties:

• Electromagnetic radiation is a form of energy that travels in waves.
• It exhibits dual nature, showing both wave and particle characteristics.
• It has electrical and magnetic components oscillating in planes perpendicular to each other and to the direction of propagation.
• It can travel through empty space.

Wave Properties:

• Wavelength ($\lambda$): The distance between two successive maxima of either electric or magnetic components. Units include meters (m), centimeters (cm), nanometers (nm), and angstroms (A°).
  • $1 nm = 10^{-7} cm = 10^{-9} m = 10 A°$
• Frequency ($v$): The number of waves passing through a fixed point per unit time. Units include cycles per second (cps), Hertz (Hz), Fresnel, kilocycles per second (kHz), and megacycles per second (MHz).
  • $1 Hz = 1 cps$
  • $1 Fresnel = 10^{12} Hz$
  • $1 MHz = 10^3 kHz = 10^6 Hz$
• Wave number ($\bar{v}$): The reciprocal of wavelength. Unit is reciprocal of distance (cm$^{-1}$).
• Velocity ($c$): The product of wavelength and frequency.
  • $λ × v = c$
  • The velocity of light in a vacuum is approximately $3 × 10^8 m/s$.

Particle Properties:

• Electromagnetic radiation consists of discrete packets of energy called photons or quanta.
• Photons have definite energy and travel in the direction of propagation at the speed of light.
• The energy of a photon ($E_p$) is proportional to the frequency of radiation:
  • $E_p = hν = \frac{hc}{λ}$
  • Where:
    • $E_p$ is the energy of the photon in Joules.
    • $v$ is the frequency of the photon.
    • $h$ is Planck’s constant ($6.626 × 10^{-34}$ Joule-second or $6.624 × 10^{-27}$ erg-seconds).
    • $c$ is the velocity of light in a vacuum.
    • $λ$ is the photon's wavelength.
• The intensity of a beam of radiation is proportional to the number of photons per second but not dependent on the energy of each photon.
• Wave characteristics explain refraction, reflection, reinforcement, and destructive interference.
• Particle characteristics explain the photoelectric effect.

Electromagnetic Spectrum

The electromagnetic spectrum results from the interaction of electromagnetic radiation with matter, leading to variations in intensity with frequency or wavelength via absorption or emission of radiation in discrete amounts (quanta). Spectroscopy measures these absorption or emission radiations to determine energy level changes.

Numericals based on energy of photon

A photon is defined as a quantum of energy. The energy of a photon ($E<em>p$) is given by, $E</em>p = hv = \frac{hc}{λ}$

Where,
$h$ = Planck’s constant ($6.624 x 10^{-27}$ erg-sec or $6.626 x 10^{-34}$ J-sec)
$v$ = Frequency of radiation
$\lambda$ = Wavelength of radiation
$c$ = Velocity of light ($3 x 10^{10}$ cm/s or $3 x 10^{8}$ m/s)

The energy, E, of an Avogadro number (N) of photons is referred to as one einstein, given by,
$E = \frac{Nhc}{λ}$

Where N = Avogadro number ($6.023 x 10^{23}$)

Energy per einstein is also called as energy in one mole of photon. Unit of energy is erg or J

• The energy, E, of an Avogadro number (N) of photons is referred to as one einstein, given by:
  • $E = \frac{Nhc}{λ}$, where N = Avogadro number ($6.023 × 10^{23}$).
  • Energy in one mole of photons is also known as Energy per Einstein.

Units of energy are ergs or Joules.

Conversions:

• $1 cal = 4.184 J$
• $1 Kcal = 1000 cal$ and $1 KJ = 1000 J$
• $1 mole = 6.023 × 10^{23}$
• $1 nm = 10^{-7} cm = 10^{-9} m = 10 A°$

Solved Numericals:

1. Calculate the energy associated with (a) one photon; (b) one einstein (or energy in one mole of photon) of radiation of wavelength 8000 A°. (h = 6.62 x 10$^{-27}$ erg-sec; c = 3 x 10$^{10}$ cm/s. N = 6.023 x 10$^{23}$).

   Solution:

   1 A° = 10$^{-8}$ cm, ∴ 8000 A° = 8000 x 10$^{-8}$ cm

   (a) Energy of a photon = $\frac{hc}{λ} = \frac{6.62 x 10^{-27} x 3 x 10^{10}}{8000 x 10^{-8}} = 2.4825 x 10^{-12} erg$

   (b) Energy per einstein, E = $\frac{Nhc}{λ} = \frac{6.023 x 10^{23} x 6.62 x 10^{-27} x 3 x 10^{10}}{8000 x 10^{-8}} = 1.4952 x 10^{12} erg$

2. Calculate the energy associated with (i) one photon; (ii) one Einstein (or energy in one mole of photon) of radiation of wavelength 7000 A°. Also, express the answer in Kcal/mole. (h = 6.626 x 10$^{-34}$ J-sec; c = 3 x 10$^{8}$ m/s. N = 6.023 x 10$^{23}$).

   Solution:

   1 A° = 10$^{-10}$ m, ∴ 7000 A° = 7000 x 10$^{-10}$ m

   (i) Energy of a photon = $\frac{hc}{λ} = \frac{6.626 x 10^{-34} x 3 x 10^{8}}{7000 x 10^{-10}} = 2.8397 x 10^{-19} J$

   (ii) Energy per einstein, E = $\frac{Nhc}{λ} = \frac{6.023 x 10^{23} x 6.626 x 10^{-34} x 3 x 10^{8}}{7000 x 10^{-10}} = 1.7104 x 10^{5} J$

   (iii) As 1 cal = 4.184 J or 4.184 J = 1 cal

   1. 7104 x 10$^{5}$ J = $\frac{1.7104 x 10^{5} x 1}{4.184} = 4.0727 x 10^{4} cal$

   l Kcal = 1000 cal or 1000 cal = 1 Kcal

   1. 0727 x 10$^{4}$ cal = $\frac{4.0727 x 10^{4} x 1}{1000} = 4.0727 x 10 = 40.727 Kcal$

   Thus, energy of wavelength = 40.727 Kcal/mole

3. The energy for a quantum of light is 4.4 x 10$^{-19}$ J. What is the wavelength and frequency of this light? (Given: h = 6.626 x 10$^{-34}$ J-s, c = 3 x 10$^{8}$ m/s)

   Solution:

   (i) Energy of a quantum = $\frac{hc}{λ}$

   ∴ λ = $\frac{hc}{Energy of a quantum} = \frac{6.626 x 10^{-34} x 3 x 10^{8}}{4.4 x 10^{-19}} = 4.5177 x 10^{-7} m$

   (ii) λ x v = c

   ∴ v = $\frac{c}{λ} = \frac{3 x 10^{8}}{4.5177 x 10^{-7}} = 6.6405 x 10^{14} cps$

Spectroscopy

Definition:

Spectroscopy is the study of the interaction between electromagnetic radiation and matter.

Principle:

Spectroscopy measures the variation in the intensity of electromagnetic radiation with frequency or wavelength after interaction with a substance. This variation occurs due to absorption or emission of radiation by the matter.

• Absorption Spectroscopy: Molecules transition from a ground state to an excited state.
• Emission Spectroscopy: Molecules transition from an excited state to a ground state.
• The plot of absorption against wavelength is called absorption spectrum.
• The plot of emission against wavelength is called emission spectrum.

If $∆E = hν = E<em>2 – E</em>1$ is the energy difference between the two molecular levels ($E<em>1$ and $E</em>2$):

• In absorption spectroscopy, a molecule absorbs a photon of energy $hv$ to transition from a lower energy level ($E<em>1$) to a higher energy level ($E</em>2$).
• In emission spectroscopy, a molecule emits a photon of energy $hv$ to transition from a higher energy level ($E<em>2$) to a lower energy level ($E</em>1$).

Classification of Spectroscopy

Spectroscopy is classified into atomic and molecular spectroscopy based on the types of energy changes within the molecule.

Types of Energy in Molecules:

• Translational Energy ($E_t$): Overall movement along three axes (not quantized).
• Electronic Energy ($E_e$): Changes in electron distribution to higher levels upon energy absorption.
• Vibrational Energy ($E_v$): Vibrations within the molecule (stretching and bending of bonds).
• Rotational Energy ($E_r$): Spinning of molecules about axes through the center of gravity.

The internal energy (E) of the molecule is due to the sum of electronic ($E<em>e$), vibrational ($E</em>v$) and rotational ($E_r$) motions within the molecule.

• $E = E<em>e + E</em>v + E_r$

Atomic Spectroscopy:

Deals with the interaction of electromagnetic radiation with atoms, typically in the ground state.

• Electronic absorption occurs when photon energy equals the energy difference between two quantized energy levels:
  • $∆E = hν$ Where:
    • $∆E$ is the energy difference between two quantum levels,
    • h is the Planck’s constant and
    • ν is frequency of photon.
• Provides qualitative and quantitative elemental analysis.

Molecular Spectroscopy:

Involves the interaction of electromagnetic radiations with molecules, leading to electronic, rotational, and vibrational transitions.

• Provides information about the structure of the molecule.
• Includes ultraviolet and infra-red spectroscopy.

Differences between Atomic and Molecular Spectra

Types of Spectroscopy

• Absorption Spectroscopy: Light is passed through an absorbing substance and then absorbed.
• Emission Spectroscopy: A substance is heated to a high temperature, emitting light that is examined with a spectroscope.
• Scattering Spectroscopy: Based on scattering phenomenon; can be elastic (wavelength unchanged) or inelastic (wavelength changed).

Electromagnetic Spectrum

An ordered arrangement of electromagnetic radiation by wavelength, ranging from gamma rays to radio waves.

Electromagnetic spectrum is an ordered arrangement of electromagnetic radiation over the entire range of wavelength. It ranges from the gamma region to the radio region, in order of increasing frequency and decreasing wavelength. As you go from left to right, the wavelengths get smaller, and the frequencies get higher. This is an inverse relationship between wave size and frequency (as one goes up, the other goes down.)

Relation between Types of Spectroscopy, Frequency, Wavelength Range and Photon Energy

The information regarding the type of spectroscopy, source of electromagnetic radiation, energy changes and applications associated with particular spectroscopy is given in Table-2.

Source, Energy Changes and Applications of Spectroscopy

Flame Photometry

Based on the principle of emission spectroscopy, it measures the intensity of light emitted when a metal is introduced into a flame.

Principle:

A liquid sample containing a metallic salt solution is aspirated into a flame. The solvent evaporates, and the metal is atomized. The heat of the flame excites valence electron/s from lower energy state ($E<em>0$) to a higher energy state ($E</em>1$).
$Na^+ + e^- \rightarrow Na$
The excited electron returns to the ground state, emitting light energy ($hv$) at a characteristic wavelength for each metal.
$E<em>1 – E</em>0 = hν$
Where h is the Plank’s constant and v is the frequency of the emitted light, defined as,
$v = \frac{c}{λ}$
Substituting for v in equation (1),
$E<em>1 – E</em>0 = \frac{hc}{λ}$
$\therefore λ = \frac{hc}{E<em>1 – E</em>0}$

The intensity of emitted light is directly proportional to the concentration of the sample. The quantity of atoms excited depends upon the temperature of the flame. Hence, more number of atoms get excited if the temperature of the flame is increased. Hence, the temperature of the flame needs to be controlled and should be uniform while performing the experiment.

Instrumentation:

Flame photometers include a burner (flame source), nebulizer, monochromator (optical system), slit system, filter, detector, and recorder.

• Burner: Maintains a constant temperature. Total consumption burners and Laminar flow burners are examples.
  • Total consumption burner - Due to the high pressure of fuel and oxidant the sample solution is aspirate through capillary and burnt at the tip of burner. Advantage over other is the entire consumption of sample. Its disadvantage is the production of non-uniform flame and turbulent. Hydrogen and oxygen are generally employed as fuel and oxidant.
  • Premix burner - In this burner the sample, fuel oxidant are thoroughly mixed before aspiration and reaching to flame. The main advantage of is the uniformity of flame produced. The main disadvantage is the heavy loss of mix up to 95%.
• Nebulizer: Sends homogeneous solution at a balanced rate. (Jet, Ultrasonic and Mesh)
  • Jet-This uses compressed gas to make an aerosol (tiny particles of medication in the air).
  • Ultrasonic-This makes an aerosol through high-frequency vibrations. The particles are larger than with a jet nebulizer.
  • Mesh-Liquid passes through a very fine mesh to form the aerosol. This kind of nebulizer puts out the smallest particles. It’s also the most expensive.
• Optical System: Includes convex mirrors and lenses to transmit and focus light.
• Filter: Isolates the desired wavelength from irrelevant emissions using a filter wheel.
• Photo-detector: Measures the intensity of radiation emitted and is either photo voltaic cell or photo tubes. In a flame spectrophotometer, photomultiplier tube is used as detector.

Working:

The sample is aspirated into the flame via a nebulizer, which creates an aerosol. The flame decomposes the sample into atoms, and valence electrons are excited. The emitted light passes through a monochromator and filter, then is detected by a photomultiplier detector. Temperature of about 2000-3000°C is obtained due to which excitation of valence electron/s takes place.

Applications:

• Qualitative Analysis: Identification of Group I and II elements (Na, K, Rb, Cs) by their characteristic wavelengths.
• Quantitative Analysis: Determination of unknown sample concentrations by comparing emission intensity to a calibration curve.
• Clinical Laboratory: Determining Na+ and K+ concentrations in biological fluids (serum, urine).
• Agriculture: Analysis of soil fertilizer requirements.
• Water Technology: Determination of calcium in hard water.
• Metallurgy: Determination of sodium in aluminum alloys.

Interferences

• Spectral Interferences: Occur due to unresolved emission lines or background flame emissions.
• Ionic Interferences: Result from ionization of metal atoms in high-temperature flames (e.g., Sodium).
• Chemical Interferences: Reactions between interferents and the analyte.
  • Cation-Anion Interference: Anions like oxalate, phosphate, sulphate may affect the intensity of radiation emitted by an element.
  • Cation-Cation Interference: Aluminium interferes with calcium and magnesium.

Disadvantages:

• Insufficient energy for excitation of transition metals.
• Cannot directly detect inert gases.
• Does not provide information about molecular structure.
• Limited to liquid samples.
• Cannot be used for the direct determination of each and every metal atom.
• The elements such as carbon, hydrogen and halides cannot be detected due to their non-radiating nature.

Jablonski Diagram

A diagram representing how molecules dissipate energy after light absorption, either through radiative or non-radiative modes. It is foundation of understanding energy dissipation processes in molecules.

Non-Radiative Transitions:

• Vibrational Relaxation: Excited molecules lose energy through collisions and descend to the lowest vibrational level of the excited state (S1).
• Internal Conversion (IC): Molecules return to the ground state by giving energy to vibrations or solvent molecules. Excess energy is lost through molecular collisions and heat is produced. It is a slow process. It may also result in a photochemical reaction.
• Intersystem Crossing: Transition from S1 to T1 (triplet state) involves spin inversion.

Radiative Transitions:

• Fluorescence: Emission of radiation as molecules return from the lower vibrational states of S1 to any vibrational state in S0, without spin inversion.
• Phosphorescence: Emission of radiation as molecules return from the T1 state to any vibrational state in S0.

Fluorescence and Phosphorescence

They are photophysical processes where molecules absorb and re-emit radiations. During excitation, the electrons move from ground to excited state. The electrons may have singlet or triplet spin states. A singlet state is a system in which all electrons are paired (have anti-parallel spins) and triplet state is one in which electrons are not paired (have parallel spins).

Fluorescence: Immediate emission of light upon excitation. Examples include quinine sulphate (blue) and chlorophyll in ether (blood red).

Phosphorescence: Delayed emission of light (delayed fluorescence) that continues after the excitation source is removed. It cannot be observed in solution at room temperature. Examples include sulphates of calcium and barium, and fluorescein in boric acid.

Comparison of Fluorescence and Phosphorescence

Applications of Fluorescence in Medicine:

• Direct determination of sulphur in protein.
• Determination of chloride in blood serum.
• Determination of strontium in blood serum and bone tissue.
• Elemental analysis of tissue, bones, and body fluids.
• Diagnosis of human diseases (cancer, skin and eye diseases, cardiovascular disease).
• Potential diagnostic tool for microorganisms.