Spectroscopy and Its Applications: An Introduction PDF

# SPECTROSCOPY AND ITS APPLICATIONS: AN INTRODUCTION ## Chapter 1: Introduction ### Syllabus - **UV/Visible Spectroscopy:** Selection rules; Line widths and intensity of spectral lines; Principle and instrumentation; Electronic Transitions; Chromophores and auxochromes; Factors affecting λ<sub>ma...

# SPECTROSCOPY AND ITS APPLICATIONS: AN INTRODUCTION ## Chapter 1: Introduction ### Syllabus - **UV/Visible Spectroscopy:** Selection rules; Line widths and intensity of spectral lines; Principle and instrumentation; Electronic Transitions; Chromophores and auxochromes; Factors affecting λ_max and intensity of spectral lines; Franck-Condon principle; Applications. - **IR Spectroscopy:** Principle and instrumentation; Vibrational frequency; Fundamental modes of vibrations and types; Anharmonics; Factors affecting vibrational frequency; Applications. - **NMR Spectroscopy:** Principle and Instrumentation; Chemical shift; Spin-Spin Splitting; High resolution NMR spectrum (PMR only). ### 1.1 INTRODUCTION Spectroscopy is the study of transitions occurring in a molecule when it interacts with electromagnetic radiations. When a radiation interacts with matter, it transfers its energy to the molecules of matter, thereby exciting the molecules to excited states. The molecules of different substances will undergo different types of transitions depending on the energy of the incident radiation. Molecular spectroscopy deals with different types of transitions occurring in various compounds. The analysis of these transitions helps in finding the structure and properties of molecules. Molecular spectroscopy is a very powerful tool for the identification of unknown compounds, determination of impurities in a sample, determination of rates of reactions and distinguishing between cis and trans isomers. ### 1.2 ELECTROMAGNETIC SPECTRUM The arrangement of all types of radiations in order of their increasing wavelength or decreasing frequency is called the electromagnetic spectrum. - The electromagnetic spectrum consists of a wide variety of radiations ranging from high energy cosmic and γ-rays to low energy microwave and radio waves. The visible radiation forms only a small portion of the electromagnetic spectrum. - A particular type of spectra can be studied using a particular type of electromagnetic radiation. Table 1.1 depicts the different regions of the electromagnetic spectrum and the type of spectra which can be studied using a particular radiation. | Electromagnetic radiation | Wavelength | Frequency | Spectrum | |---|---|---|---| | Radio frequency region | 100m - 1cm | 10⁶- 10¹⁰ Hz | Nuclear Magnetic Resonance (NMR), Electronic Spin Resonance (ESR) | | Microwave region | 1cm - 100 μm | 10¹⁰-10¹² Hz | Microwave Spectroscopy (Rotational Spectroscopy) | | Infra-red region | 100 μm - 1 μm | 10¹²-10¹⁴ Hz | Infrared Spectroscopy (Vibrational Spectroscopy) | | Visible and Ultraviolet region | 1 μm - 10 nm | 10¹⁴-10¹⁶ Hz | Ultraviolet-Visible Spectroscopy (Electronic Spectroscopy) | | X-ray region | 10 nm - 100 pm | 10¹⁶-10¹⁸ Hz | Photo - electron Spectroscopy (PES) | | γ-ray region | 100 pm - 1 pm | 10¹⁸-10²⁰ Hz | Mossbauer Spectroscopy | (1 μm = 10^-6 m, 1 nm = 10^-9 m, 1 pm = 10^-12 m) ### 1.3 ELEMENTARY IDEAS ABOUT ELECTROMAGNETIC RADIATIONS - Fields associated with electromagnetic radiation are perpendicular to each other and to the direction of movement of radiation. - All types of electromagnetic radiations travel with the same velocity and no medium is required for their propagation. They can travel through a vacuum also. - The three main terms depicting the nature of an electromagnetic radiation are as follows: - **Wavelength:** Wavelength is the distance between two adjacent crests (maxima point) or troughs (minimum point). It is denoted by λ. It is normally measured in the units of nm or ź.(1 nm = 10^-9 m, 1ź = 10^-8 m) - **Wave number:** Wave number is the number of waves which can pass through a space of one cm. It is the reciprocal of wavelength and is expressed in per centimeter (or cm^-1). It is denoted by ν. $$ν = \frac{1}{λ}$$ - **Frequency:** Frequency is the number of waves which can pass through a point in one second. It is expressed in cycles per second or Hertz (Hz) and is denoted by symbol ν. - These three quantities are related by the following relation $$ν = \frac{c}{λ}$$ - The energy carried by an electromagnetic radiation is directly proportional to its frequency. The emission and absorption of radiation is quantized and each quantum of radiation is called a photon. The energy of a photon (E) is given by: $$E = hν = \frac{hc}{λ} = hcν$$ - Where h is Planck’s constant, h = 6.626 × 10^-34 Joule second (Js) = 6.626 × 10^-27 ergs second ### 1.4 ABSORPTION AND EMISSION SPECTRUM - All the molecules have quantized energy levels i.e. each energy level possesses definite amount of energy. When an electromagnetic radiation falls on a molecule present in the ground state energy level then the molecule undergoes transition to the excited state. - Consider E₀ and E₁ are the energies of ground state and excited state respectively. The electromagnetic radiation will be able to excite the molecule from the ground state to the excited state if the energy of electromagnetic radiation is equal to the energy difference (ΔE = E₁ – E₀). The spectrum obtained by the transition of a molecule from its ground state to its excited state is called the absorption spectrum. (Fig 1.2a). - ΔE = E₁ – E₀ = hv = hc/λ - When the molecule falls from the excited state to the ground state it emits a photon of energy hv. The spectrum obtained by the transition of a molecule from its excited state to the ground state is called the emission spectrum. ### 1.5 ATOMIC AND MOLECULAR SPECTROSCOPY - Spectroscopy is divided into two types (a) Atomic spectroscopy (b) Molecular spectroscopy. #### 1.5.1 Atomic Spectroscopy - The atomic spectrum is obtained when the atoms in the ground state are excited to higher states by the incident electromagnetic radiation. Each atom gives its own characteristic spectrum in the form of lines called a line spectrum. - The characteristic line spectrum obtained in case of an atom is due to the electronic transitions between the energy levels. #### 1.5.2 Molecular Spectroscopy - Molecular spectroscopy refers to the interaction of electromagnetic radiation with molecules. - As compared to the atomic spectrum which results due to electronic transitions, the molecular spectrum is obtained due to three types of transitions namely, rotational, vibrational and electronic transitions. So, the spectra of molecules is complex as compared to that of atoms. - According to the Born-Oppenheimer approximation, the total energy (E) of a molecule is the sum of translational energy (E_tr), rotational energy (E_rot), vibrational energy (E_vib) and electronic energy (E_el) - Further - E = E_tr + E_rot + E_vib + E_el - E_el >> E_vib >> E_rot >> E_tr - The translational energy is not quantized and also the amount of translational energy is negligibly small, so the total energy of the molecule may be given by: - E = E_rot + E_vib + E_el - The origin of different types of energies can be conveniently explained by taking the example of a diatomic molecule. The rotational energy arises when the diatomic molecule rotates about an axis passing through the centre of gravity of a molecule and perpendicular to the internuclear axis. Vibrational energy is associated with the to and fro motion of the molecule. - These different types of energies are represented with the help of different energy levels as shown in Fig. 1.3. In Fig. 1.3, two electronic energy levels ie, the ground state (E₀) and an excited state (E₁) electronic energy levels are shown. With each electronic energy level, a series of vibrational energy levels are associated. These vibrational energy levels are designated by vibrational quantum number ‘v’. Further, with each vibrational energy level, a series of rotational energy levels are associated. These rotational energy levels are designated by rotational quantum number ‘J’. - It is customary to use a single prime superscript to designate a higher energy level and a double prime to designate a lower energy level. - Accordingly, vibrational energy levels of the ground state electronic energy level are designated by ν” = 0, ν” = 1, ν” = 2, ν” = 3 etc. and vibrational energy levels of an excited state electronic energy level are designated by ν’ = 0, ν’ = 1, ν’ = 2, ν’ = 3 etc. - Similarly, rotational energy levels of the ground state electronic energy level are designated by J” = 0, J” = 1, J” = 2, J” = 3, etc, and rotational energy levels of an excited state electronic energy level are designated by J’ = 0, J’ = 1, J’ = 2, J’ = 3 etc. - The transitions between the ground electronic energy level and excited electronic energy levels give rise to electronic spectra. The electronic spectra are obtained with ultraviolet and visible radiations. Hence it is also called ultraviolet-visible spectra (UV-visible spectra). ### 1.6 TYPES OF MOLECULAR SPECTRA - Depending on the frequency of incident radiation, the different types of spectra may be obtained. The major types of spectra given by a molecule and the region of electromagnetic radiation involved are briefly explained below: 1. **Rotational Spectra (Microwave Spectra):** The rotational spectrum is obtained due to transition between the rotational energy levels on the absorption of microwave radiations. As microwaves possess very low energy, so they can bring about transitions between the rotational energy levels only. So, a pure rotational spectrum is obtained which is also called microwave spectra. Microwave spectra are produced by microwaves having a wavenumber (ν) in the range 1-100 cm^-1. 2. **Vibrational Spectra (Infrared Spectra):** The vibrational spectrum is obtained due to transition between the vibrational energy levels on the absorption of Infrared radiations. The vibrational spectrum is also called Infrared spectra (IR spectra). Vibrational spectra are produced by Infrared radiations having a wavenumber (ν) in the range 667-4000 cm^-1. 3. **Electronic Spectra:** The electronic spectra are obtained due to transition between the electronic energy levels on the absorption of ultraviolet and visible radiations. Electronic spectra are produced by visible radiations having a wavenumber (ν) in the range 12,500 – 25,000 cm^-1 and ultraviolet radiations in the range 25,000 – 70,000 cm^-1. When ultraviolet and visible radiations are incident on a molecule, the electronic transitions are accompanied by rotational and vibrational transitions. Hence, the electronic spectra consist of complex bands. 4. **Raman Spectra:** Raman spectra is based on the scattering of radiation rather than absorption of radiation. When a radiation falls on a sample, the intensity of scattered radiation is observed at right angle to the incident beam. Most of the scattered light has the same frequency as the incident beam (called Rayleigh scattering). However, some of the scattered light has different frequency than the incident radiation. This is called Raman scattering. The difference in the frequency of incident radiation and Raman scattering corresponds to vibrational and rotational transitions in the molecule. Raman spectra are observed in the visible region (i.e.) 12,500 - 25,000 cm^-1. 5. **Nuclear Magnetic Resonance (NMR) Spectra:** Nuclear Magnetic Resonance (NMR) spectrum results from the transitions between the nuclear spin energy levels of the molecule when an external magnetic field is applied on it. This spectrum is obtained in the radio frequency range 5 – 100 MHz. 6. **Electron Spin Resonance (ESR) Spectra:** Electron Spin Resonance (ESR) spectrum results from the transitions between the electron spin energy levels of the molecule when an external magnetic field is applied on it. This spectrum is obtained in the microwave frequency range 2000 - 9600 MHz. ### 1.7 EXPERIMENTAL TECHNIQUES Molecular spectroscopy deals with the interaction of electromagnetic radiation with matter. When a radiation is incident on a sample, a part of incident radiation is absorbed by the sample and the remaining part is transmitted through the sample. Hence, the incident radiation undergoes a change in its intensity. The changes in intensity of incident radiation are detected by a device called Spectrophotometer. Spectrophotometer is a device used to measure the intensity of absorbed or transmitted radiation. #### 1.7.1 Components of Spectrophotometer The different components of a spectrophotometer are: 1. **Source of electromagnetic radiation:** The different types of sources are used to generate different ranges of electromagnetic radiation. - For ultraviolet radiation, a Hydrogen / Xenon discharge lamp and Mercury arc are used as a source of radiation. - For visible region, a Tungsten filament lamp is used as a source of radiation. - For Infrared region, the source of radiation is a Nernst filament which consists of oxides of thorium and cerium maintained at a high temperature of 1500°C. - For microwaves, an electromagnetic oscillator like Klystron is used. A Klystron is a specially developed electron tube in which electrons moving towards a plate generate electromagnetic radiations. - Radiofrequency radiations are generated by oscillating electric currents in a coil of wire. 2. **Monochromator:** Before passing the radiation through a sample, the radiation is rated into its constituent frequencies by a dispersing device such as a prism or diffraction grating. The prism used for ultraviolet irradiation is a quartz prism, for visible radiations, a glass prism and for Infrared radiations, a rock salt prism is used. Generally, diffraction grating is preferred to a prism for use as a monochromator. A diffraction grating consists of a glass or ceramic plate in which fine grooves have been cut 1000 nm apart and covered with a reflective aluminum coating. 3. **Sample Holder:** It is used to hold the sample in the instrument. The sample holder is a test tube in colorimetry, a quartz cell in ultraviolet and visible spectroscopy, and a glass tube called an NMR tube in NMR spectroscopy. 4. **Detector:** The detector is a device that converts the radiation into an electric signal which is further processed by a recorder. The radiation-sensitive semiconductors are commonly used as detectors. The thermocouple detector is commonly used in the Infrared region. The photomultiplier tube is used in the visible and ultraviolet region as a detector. 5. **Amplification and recording units:** The radiation from the detector is chopped by a shutter that rotates in the beam of radiation to obtain an alternating signal from the detector. This is due to the fact that an alternating signal can be easily amplified than a steady signal. The signal amplified by the amplifier is recorded on the computer or a graphical print-out. #### 1.7.2 Single and Double Beam Spectrophotometer The single beam and double beam spectrophotometers are extensively used in spectroscopic analysis of compounds. The sample whose spectrum is to be studied is taken in a cell called a sample cell. In another cell called the reference cell, an appropriate solvent is taken. In the single beam spectrophotometer, the beam of radiation is passed through the sample solution and reference solution one by one. (Fig 1.4a) In the double beam spectrophotometer, the beam of radiation is split into two identical halves called the sample beam and reference beam, and both these beams are simultaneously passed through the sample solution and reference solution. (Fig. 1.4b) If I is the intensity of radiation coming out of the sample solution and I₀ is the intensity of radiation coming out of the reference solution, the absorbance A of the solution is given by: **Absorbance** A = log₁₀ I₀/I Further, the transmittance T of the solution is given by: **Transmittance** T = I/I₀ Hence, A = log₁₀ 1/T The absorbance (A) or transmittance (T) is directly measured by the spectrophotometer at different wavelengths. The recorder generates a graph between the wavelength of the entire region and the absorbance of light at each wavelength. This graph is called the absorption spectrum of the compound. The absorption spectrum is a characteristic property of any compound. No two compounds can have the same absorption spectra. ### 1.8 SELECTION RULES It has been stated earlier that the different types of molecular spectra are obtained by transitions taking place between energy levels. All types of transitions between all the energy levels are not possible. There are some restrictions imposed on the quantum numbers during transitions. The transitions are governed by rules called **Selection Rules**. The selection rules to be followed depend on the type of transition. The selection rules are expressed in terms of change in the quantum number in a particular type of transition. The most commonly followed selection rules are as follows: 1. **For vibrational transition,** the selection rule is Δv = ± 1, where v is the vibrational quantum number. Further Δv = + 1 corresponds to absorption and Δv = - 1 corresponds to emission. 2. **For rotational transition,** the selection rule is ΔJ = ±1, where J is the rotational quantum number. Further ΔJ = + 1 corresponds to absorption and ΔJ = - 1 corresponds to emission. 3. **For electronic transitions in atomic spectra** , selection rule is Δl = ± 1, where l is the azimuthal quantum number. Hence, the transition between a p-orbital and a d-orbital is allowed because l = 1 (for p-orbital) and l = 2 (for d-orbital) ie. Δl = +1. Similarly, the transition between an s-orbital and a d-orbital is not allowed because l = 0 (for s-orbital) and l = 2 (for d-orbital) ie. Δl = +2. It has been observed that in some cases the selection rules are not followed strictly. The transitions which are obtained by following the selection rules are called **allowed transitions**. The transitions which violate the selection rules are called **forbidden transitions**. It needs to be pointed out here that the term ‘forbidden transition’ does not mean that the transition will not take place at all. It actually refers to the fact that the probability of this transition is very less and a very weak signal will be obtained due to this transition. The **allowed transitions** are more intense and strong whereas the **forbidden transitions** are less intense and weak. ### 1.9 WIDTH & INTENSITIES OF SPECTRAL LINES In any spectra, all the signals obtained are not of equal intensity and sharpness. Generally, some signals are very sharp and other signals are broad. Similarly, some signals are very intense and others are not. The two important characteristics of a spectral line are width and intensity. The sharpness of a signal is determined by the width of the spectral line. The strength of a signal is determined by the intensity of the spectral line. These two characteristics are being explained below: #### 1.9.1 Width of Spectral Lines - If the spectral line obtained is sharp then it will have no width, whereas if the spectral line is not sharp it will have a certain width as shown in Fig. 1.5. - The width of a spectral line is defined as the width at half the value of absorption i.e. at half the height of the signal. #### FACTORS AFFECTING WIDTH OF THE SPECTRAL LINES The following are three major factors which lead to the broadening of spectral line: 1. **Natural broadening or Life-time broadening:** The natural broadening or life-time broadening can be explained on the basis of Heisenberg’s uncertainty principle given by equation (1.1). - ΔE × Δt ≥ h/4π ....(1.1) - Where: - ΔE = uncertainty in energy of an energy level - Δt = uncertainty in life-time of an energy level - Further, the energy of a quanta of radiation is given by E = hv. - ΔE = hΔν ....(1.2) - Hence, from equations (1.1) and (1.2) - hΔν × Δt ≥ h/4π - Δν ≥ 1/4πΔt - Δν is called the natural line width - Hence, the minimum value of line width is: - Δν = 1/4πΔt ....(1.3) - Further, as c = νλ - ν = c/λ = cv - Δν = cΔν ....(1.4) - So, from equations (1.3) and (1.4) - Δν = 1/4πcΔt ....(1.5) - The above equation gives the natural line width in terms of a wave number. - Substituting c = 3 × 10¹⁰ cm and π = 3.14, in equation (1.5) we get: - Δν = 1/4πcΔt = 1/(4 × 3.14× 3 × 10¹⁰ × Δt) = 5.3×10^-12 /Δt - The broadening of a signal is inversely proportional to the life-time of the excited state. A sharp signal is obtained if the life-time of the state involved in transition is high. As, generally, the excited states are unstable having small life-time, so very often the broad signals are obtained. 2. **Collision broadening:** The broadening of spectral lines due to collision broadening is observed in ultraviolet and visible spectra. When ultraviolet or visible radiation falls on a molecule, transitions take place between the outermost energy shells of the molecule. The molecules in gaseous and liquid phase collide with one another thereby deforming the electronic charge cloud of the electrons present in the outermost energy levels. Hence, different molecules of the same sample undergo transition by absorbing different frequency of the incident radiation resulting in the broad bands in spectra. - It may be noted that since molecules of solids do not vibrate strongly, so less collisions take place in solids. Hence, relatively sharp signals are generally observed in gaseous samples as the gas molecules move randomly, having a velocity relative to the observer or observing instrument. 3. **Doppler broadening:** Doppler broadening is generally observed in the gaseous samples as the gas molecules move randomly, having a velocity relative to the observer or observing instrument. - If the molecule is moving towards the instrument with velocity u, then the frequency v’ of radiation as observed by the molecule is given by: - v’ = v(1 + u/c) ....(1.6) - where v is the actual frequency of incident radiation and c is the velocity of light. - On rearranging equation (1.6), we get: - Δν = (v-v’)/v = u/c - Similarly, if the molecule is moving away from the instrument with velocity u, then the frequency v’ of radiation as observed by the molecule is given by: - v’ = v(1- u/c) ....(1.7) - On rearranging equation (1.7), we get: - Δν = (v-v’)/v = u/c - So, depending on the direction of motion of the molecule, the observed frequency becomes higher or lower than the actual frequency of radiation. Hence, the different molecules of the same sample undergo absorption at different values of frequency resulting in the broadening of the signal. - According to kinetic theory of gases, the Doppler broadening Δν is proportional to T^1/2. So, Doppler broadening can be reduced by measuring the spectra at low temperature. #### 1.9.2 Intensities of Spectral Lines The intensity of a spectral line is determined by the following two factors: 1. **Boltzmann population of energy levels** 2. **Transition probability** These two factors are explained as follows: 1. **Boltzmann population of energy levels**: According to Boltzmann, if N₀ is the number of molecules in the ground state, then the number of molecules, N, in the excited state at a temperature T is given by: - N = N₀e^-ΔE/kT ....(1.8) - Where: - ΔE is the energy difference between the ground state and excited state, and k is the Boltzmann constant. - From equation (1.8) - N/N₀ = e^-ΔE/kT - From equation (1.9), it is clear that if ΔE is large, then - N/N₀ < 1 or N < N₀ - So, the number of molecules in the excited state is less than the molecules in the ground state. So, the spectral lines originating from the transition from the ground state (E₀) to the first excited state (E₁) will be more intense as compared to the transitions from the first excited state (E₁) to the second excited state (E₂). 2. **Transition probability:** The transition probability refers to the probability of transition between two energy levels. On absorption of radiation, molecules undergo transitions to higher states. These transitions are governed by selection rules. The transitions which obey selection rules are called **allowed transitions**. The probability of allowed transitions is more and strong signals are obtained from these transitions. - The transitions which violate selection rules are called **forbidden transitions**. The probability of forbidden transitions is less and weak signals are obtained from these transitions. ## Solved Conceptual Problems **Example 1.1:** What is line width of a spectra? (P.T.U. Dec 2004) **Solution:** The width of a spectral line is defined as the width at half the value of absorption i.e., at half the height of the signal. **Example 1.2:** Why does molecular spectroscopy utilize absorption spectra and not emission spectra? (P.T.U. Dec 2002) **Solution:** In absorption spectra, the molecules absorb the incident radiation and undergo different types of transitions. These transitions are recorded by a spectrophotometer. On the other hand, emission spectra refers to the recording of emitted radiation by a molecule in the excited state. So, in emission spectra, a compound is required to be heated to a higher temperature which is not required in absorption spectroscopy. Thus absorption spectra is easy to interpret and used frequently in molecular spectroscopy. **Example 1.3:** Arrange the following electromagnetic radiations in order of increasing wavelength: Gamma rays, X-rays, ultraviolet, infrared, visible, microwaves, radiowaves (P.T.U. May 2005) **Solution:** The following is the increasing order of wavelength: - Gamma rays < X-rays < ultraviolet < infrared < visible < microwaves < radiowaves **Example 1.4:** What is Doppler broadening of spectral lines? (P.T.U. May 2001) **Solution:** Doppler broadening is broadening of spectral lines due to the random movement of molecules relative to the observer or observing instrument. Depending on the direction of motion of the molecule, the observed frequency becomes higher or lower than the actual frequency of radiation. Hence, the different molecules of the same sample undergo absorption at different values of frequency resulting in the broadening of the signal. **Example 1.5:** Define wave number. What are its units? (P.T.U. Dec 2007) **Solution:** Wave number (ν) is the number of waves which can pass through a space of one cm. It is the reciprocal of wavelength and is expressed in per centimeter (cm-¹). Wave number ν = 1/λ. The units of wave number are cm^-1 or m^-1.