Principles of Spectroscopy

1. Introduction to Spectroscopy

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

When electromagnetic radiation interacts with atoms or molecules, energy may be:

Absorbed
Emitted
Scattered

These processes occur when electrons or nuclei move between different energy levels.

Spectroscopic techniques help scientists:

Determine molecular structure
Study energy levels of atoms and molecules
Identify chemical compounds
Measure concentration of substances

The instruments used in spectroscopy are called spectrometers or spectrophotometers.

2. Electromagnetic Radiation

Electromagnetic radiation consists of oscillating electric and magnetic fields that travel through space at the speed of light.

According to Maxwell’s theory, electromagnetic waves contain:

Electric field (E)
Magnetic field (B)

Both fields are perpendicular to each other and to the direction of propagation.

Speed of electromagnetic radiation in vacuum:

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

Electromagnetic radiation shows dual nature:

Wave nature
Particle nature (photons)

3. Important Characteristics of Electromagnetic Radiation

1. Wavelength (λ)

Distance between two successive crests or troughs of a wave.

Units used:

meters (m)
nanometer (nm)
angstrom (Å)
micrometer (µm)

Example:

1 Å = $10^{-10}$ m

2. Frequency (ν)

Number of waves passing through a point per second.

Unit: Hertz (Hz)

ν = \frac{c}{λ​}

Where:

$\nu$ = frequency
$c$ = velocity of light
$\lambda$ = wavelength

3. Wave Number (ṽ)

Number of waves per centimeter.

\overset{ˉ}{ν} = \frac{1}{λ​}

Unit:

c m^{- 1}

Wave number is widely used in infrared spectroscopy.

4. Energy of Radiation

Energy of a photon is given by:

E = h ν

Where:

h

= Planck’s constant

$\nu$ = frequency

Energy can also be written as:

E = \frac{h c}{λ​}

4. Electromagnetic Spectrum

Electromagnetic radiation covers a wide range of wavelengths and frequencies.

Order of increasing wavelength

Gamma rays → X-rays → UV → Visible → IR → Microwaves → Radio waves

Order of increasing energy

Radio waves → Microwaves → IR → Visible → UV → X-rays → Gamma rays

5. Interaction of Radiation with Matter

When electromagnetic radiation interacts with matter, several phenomena occur.

1. Reflection

Light bounces back from a surface.

2. Refraction

Change in direction of light when it passes from one medium to another.

3. Diffraction

Bending of light around obstacles.

4. Scattering

Light is redirected in different directions.

Types:

Rayleigh scattering – same frequency
Raman scattering – different frequency

5. Absorption

Energy from radiation is absorbed by molecules.

6. Emission

Excited molecules release energy in the form of radiation.

6. Molecular Energy Levels

Molecules possess different types of energy.

Total molecular energy is:

E_{t o t a l} = E_{t r a n s} + E_{r o t} + E_{v i b} + E_{e l e} + E_{s p i n} + E_{n u c l e a r​}

Where:

Translational energy
Rotational energy
Vibrational energy
Electronic energy
Spin energy
Nuclear energy

Usually:

E_{e l e c t r o n i c} > > E_{v i b r a t i o n a l} > > E_{r o t a t i o n a l​}

7. Born–Oppenheimer Approximation

This approximation assumes that:

Electron motion and nuclear motion can be treated separately.

Reason:

Nuclei are much heavier than electrons.
Electrons move much faster.

Thus molecular energy can be simplified as:

E = E_{e l e c t r o n i c} + E_{v i b r a t i o n a l} + E_{r o t a t i o n a l​}

8. Types of Molecular Spectra

Molecular spectra arise from transitions between different energy levels.

1. Rotational Spectra

Occur due to transitions between rotational energy levels
Observed in microwave region
Only molecules with permanent dipole moment show rotational spectra

Examples:

HCl, CO, NO

2. Vibrational Spectra

Transitions between vibrational energy levels.

Observed in:

Infrared region

Occurs only when dipole moment changes during vibration.

Example:

CO₂ shows IR absorption.

3. Electronic Spectra

Transitions between electronic energy levels.

Observed in:

UV region
Visible region

These spectra are usually complex because vibrational and rotational transitions occur simultaneously.

9. Atomic Spectra

When atoms absorb or emit radiation, they produce line spectra.

Each line corresponds to a transition between two electronic energy levels.

Thus atomic spectra provide information about:

Atomic structure
Energy levels of electrons

10. Selection Rules

Not all transitions between energy levels are allowed.

Rules that determine allowed transitions are called selection rules.

For electric dipole transitions:

Transition is allowed only if the transition moment integral is not zero.

Allowed transitions produce strong spectral lines, while forbidden transitions produce weak lines.

11. Spectral Bands

A spectral band is characterized by:

Position
Intensity
Shape
Width

Spectral lines are not infinitely sharp due to line broadening.

12. Band Width

Band width is defined as:

Width of the band at half of its maximum intensity.

Denoted as:

Δ ν_{1 / 2​}

13. Factors Affecting Spectral Line Width

1. Natural Broadening

Due to uncertainty principle.

Δ E Δ t \geq \frac{h}{4 π​}

Shorter lifetime → broader spectral line.

2. Doppler Broadening

Caused by motion of molecules relative to the observer.

Moving molecules cause shift in frequency.

3. Collision Broadening

Frequent collisions between molecules cause:

Disturbance in energy levels
Broadening of spectral lines

4. Pressure Broadening

Higher pressure increases collisions between molecules, leading to broader spectral lines.

14. Line Shapes

Two common spectral line shapes are:

Lorentzian profile

Occurs due to lifetime broadening.

Gaussian profile

Occurs due to Doppler broadening.

15. Intensity of Spectral Lines

Intensity depends on three factors:

Transition probability
Population of molecules in energy levels
Concentration of the sample

16. Boltzmann Distribution

Population of molecules in different energy levels follows Boltzmann distribution.

\frac{N_{u p p e r}}{N_{l o w e r}} = e^{- Δ E / k T}

Where:

$N$ = number of molecules
$k$ = Boltzmann constant
$T$ = temperature

17. Einstein Coefficients

Three coefficients describe transitions between energy levels.

1. $B_{lm}$

Stimulated absorption coefficient.

2. $B_{ml}$

Stimulated emission coefficient.

3. $A_{ml}$

Spontaneous emission coefficient.

Relation between coefficients:

\frac{A_{l m}}{B_{l m}} = \frac{8 π h ν^{3}}{c^{3​}}

18. Energy Dissipation from Excited States

Excited molecules lose energy by two processes:

1. Radiative Process

Energy released as radiation.

Example:

Fluorescence

2. Non-Radiative Process

Energy transferred to other molecules as heat.

Occurs through:

Molecular collisions
Vibrational relaxation

19. Relaxation Time

Relaxation time is the time taken for an excited molecule to return to ground state.

Typical values:

Electronic states:

10^{- 6} - 10^{- 8} s

Vibrational states:

10^{- 1} - 10^{- 3} s

20. Instrumentation in Spectroscopy

A typical spectrometer consists of:

Source of radiation
Sample holder
Monochromator or analyzer
Detector
Recorder or computer

Flow of operation:

Source → Sample → Analyzer → Detector → Recorder

21. Absorption Spectrometer

Used for measuring absorption spectra.

Radiation passes through the sample and the transmitted light is measured.

22. Emission Spectrometer

Measures radiation emitted by excited atoms or molecules.

Used in flame spectroscopy and atomic emission spectroscopy.

23. Spurious Radiation

Sometimes unwanted radiation reaches the detector.

This is called spurious radiation.

Sources include:

Dust particles
Reflection from optical parts
Scattering in air

It can be minimized by:

Using baffles
Black coating inside instruments
Preventing dust entry

Key Points to Remember

Spectroscopy studies interaction of radiation with matter.
Energy of radiation is quantized.
Molecular spectra arise from rotational, vibrational, and electronic transitions.
Spectral lines are affected by Doppler, collision, and pressure broadening.
Spectroscopy is widely used for structure determination and chemical analysis.

Learn more about Spectroscopy at-

All Spectroscopy Resources

Share with your friends to spread free science and chemistry education to all...

Provide feedback below.... Learn, Grow & Shine

Explore our Science Book at

Amazon.com Book Store | Amazon.in Book Store | Author Page | Flipkart Book Store | NotionPress Book Store

Explore our Science Book in Hindi Language at

Amazon.com Book Store | Amazon.in Book Store | NotionPress Book Store | Author Page | Flipkart Book Store

Principles of Spectroscopy

Principles of Spectroscopy

1. Introduction to Spectroscopy

2. Electromagnetic Radiation

3. Important Characteristics of Electromagnetic Radiation

1. Wavelength (λ)

2. Frequency (ν)

3. Wave Number (ṽ)

4. Energy of Radiation

4. Electromagnetic Spectrum

Order of increasing wavelength

Order of increasing energy

5. Interaction of Radiation with Matter

1. Reflection

2. Refraction

3. Diffraction

4. Scattering

5. Absorption

6. Emission

6. Molecular Energy Levels

7. Born–Oppenheimer Approximation

8. Types of Molecular Spectra

1. Rotational Spectra

2. Vibrational Spectra

3. Electronic Spectra

9. Atomic Spectra

10. Selection Rules

11. Spectral Bands

12. Band Width

13. Factors Affecting Spectral Line Width

1. Natural Broadening

2. Doppler Broadening

3. Collision Broadening

4. Pressure Broadening

14. Line Shapes

Lorentzian profile

Gaussian profile

15. Intensity of Spectral Lines

16. Boltzmann Distribution

17. Einstein Coefficients

1. BlmB_{lm}​

2. BmlB_{ml}​

3. AmlA_{ml}​

18. Energy Dissipation from Excited States

1. Radiative Process

2. Non-Radiative Process

19. Relaxation Time

20. Instrumentation in Spectroscopy

21. Absorption Spectrometer

22. Emission Spectrometer

23. Spurious Radiation

Key Points to Remember

Learn more about Spectroscopy at-

You might like

1. $B_{lm}$

2. $B_{ml}$

3. $A_{ml}$