CHEM Atomic and Molecular Spectroscopy

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1 CHEM Atomic and Molecular Spectroscopy References: 1. Fundamentals of Molecular Spectroscopy by C.N. Banwell 2. Physical Chemistry by P.W. Atkins Dr. Sujeewa De Silva

2 Sub topics Light and matter Polarizability and molar polarization Molecular Spectroscopy Vibrational spectroscopy Rotational spectroscopy Raman spectroscopy Electronic Spectroscopy

3 Spectroscopy, in general -is the study of light interaction with matter Interactions between light and matter determine the appearance of everything around us

4 Light & Matter can interact in a number of different ways: Matter can transmit light (glass, water). Matter can reflect or scatter light. Matter can gain energy by absorbing light. Matter can lose energy by emitting light.

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7 Movie screen scatters light from the projector in all directions Interactions between light and matter determine the appearance of everything around us

8 Absorb radiation Black surface Reflects radiation White surface Transmit all radiation Colourless surface

9 Wavelength (nm) Colour Absorbed Colour Observed Violet Green-Yellow Violet-Blue Yellow Blue Orange Blue-Green Red Green Purple Yellow-Green Violet Yellow Violet-Blue Orange Blue Red Blue-Green Purple Green

10 CuSO 4 solution Emit blue radiation Absorb red/orange light

11 The Bunsen burner is used for elemental analysis. Li Na K

12 e - can have only specific (quantized) energy values

13 Energy levels or "shells exist for electrons in atoms and molecules. Evidences: Observations of light emitted by the elements is one evidence for the existence of shells, subshells and energy levels. (Flame Test) The brilliant colors of fireworks result from jumps of electrons from one shell to another of mixture of metal atoms in explosive powder.

14 Bohr s Model of the Atom (1913) 1. e - can have only specific (quantized) energy values 2. light is emitted as e - moves from higher energy level to a lower energy level n (principal quantum number) = 1,2,3, R H (Rydberg constant) = 2.18 x J

15 The Bohr Model of the Atom excited state The atom is less stable in an excited state and so it will release the extra energy to return to the ground state ground state

16 Electromagnetic Radiation (EMR)

17 Electromagnetic radiation Electromagnetic radiation is an energy wave that is composed of an electric field component and a magnetic field component. When radiation in the visible region falls on the human eye, it is the interaction of the electric component with the retina which results in detection. It is also the electric character of electromagnetic radiation which is most commonly involved in spectroscopy.

18 The Effect of Radiation on Atoms and Molecules Atoms can absorb and emit energy in only discrete chunks (called quanta) Suggested by Max Planck ( ) All EMR / light behave as packets of energy called photons. A photon is a particle of EMR Albert Einstein ( )

19 e - can have only specific (quantized) energy values

20 EMR is a stream of photons, each traveling in a wave-like pattern, moving at the speed of light and carrying some amount of energy

21 Wavelength and Amplitude 07_02.JPG

22 Wavelength x Frequency = Speed = m x 1 s c m s c = c is defined to be the rate of travel of all electromagnetic energy in a vacuum and is a constant value speed of light. c = 3.00 x 10 8 m s -1 This speed c differs from one medium to another, but not enough to distort our calculations significantly.

23 Electromagnetic energy Einstein found a very simple relationship between the energy of a light wave E (photon) and its frequency Energy of light (E) = h h - Planck's constant'' = Js c = or` = c/ orh` = c/ E hν hc λ hcν ν 1 λ

24 E hν hc λ

25 Bluer light has shorter λ, higher frequency, and more energy. Redder light has longer λ, lower frequency, and less energy. E hν hc λ

26 What is a Spectrum? A spectrum is the distribution of photon energies coming from a light source: - Shows how many photons of each energy are emitted by the light source? Spectra are observed by passing light through a spectrograph: - Breaks the light into its component wavelengths and spreads them apart (dispersion).

27 Absorption

28 Emission

29 White light pass through a monochromator and then though the sample Detector records the intensity of transmitted light as a function of frequency

30 Atomic spectrum - less interaction between atoms in the gas phase -absorb specific wavelengths Molecular spectrum - Molecular interactions and collision leads to distribution of energy, - absorb a range of wavelengths

31 Beer-Lambert Law The Beer-Lambert law is the linear relationship between absorbance and concentration of an absorber of electromagnetic radiation. The general Beer-Lambert law: A = ε λ x b x c A - is the measured absorbance b - is the path length c - is the analyte concentration - wavelength-dependent molar absorptivity coefficient ε λ where I - is the intensity of transmitted radiation I 0 - is the intensity of incident radiation

32 Experimental measurements are usually made in terms of transmittance (T) T = I / I 0 A = log 10 (I 0 / I ) = ε λ b c The relation between A and T is: A = - log 10 (I / I 0 ) = - log 10 (T) = ε λ b c

33 Absorbance Beer-Lambert Law Concentration

34 Deviation from Bear Lambert law Low c High c The Beer-Lambert law assumes that all molecules contribute to the absorption and that no absorbing molecule is in the shadow of another

35 Some important terms

36 Dipole moment: There is a net charge separation due to different electronegativities of the atoms of a molecule +δ H Cl -δ

37 Molecular Dipole Moments (m) Molecular Dipole Moments are the vector sum of the individual bond Dipole moments. They depend on the magnitude and direction of the bond dipoles. NH 3 H 2 O CO 2 CH 3 Cl H H N H : H H O : :.... :O =C = O : H C H H Cl m 1.5 D 1.9 D 0.0 D 1.87 D

38 Potential energy When two charges q 1 and q 2 in a polar molecule, are separated by a distance r in a vacuum, the potential energy (v) of their interactions can be given by q r q 1 2 v q 1 q 4 Electric force lines produced by an electric dipole 2 0 r

39 Effect of external electric field The electrons and nuclei of molecule are mobile to a limited degree. For that reason, when a polar or non-polar molecule is placed in an electric field a small displacement of the charge will take place. As a result, a dipole would be introduced in the molecule, in addition to the permanent one that may exist. DP = µ p + µ i

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41 Polarizability and Molar Polarization Polarizability is the relative tendency of the electron cloud of an atom to be distorted from its normal shape by the presence by an external electric field (or near by ions or dipole) It is experimentally measured as the ratio of induced dipole moment (µ ind ) to the electric field E which induces it: α = µ ind / E The units of α are C 2 m 2 V 1 Polarizabilities(α) in different directions - along the bond, called longitudinal polarizability and perpendicular to the bond, called transverse polarizability

42 The molar polarization or induced polarization is given by (Debye equation) Where, p r P is the molar polarization M is the molar mass of the sample ρ is the mass density of the sample r 1 2 ε r is the relative permittivity where ε r = ε/ε 0 ε is permittivity of the medium ε 0 is vacuum permittivity M

43 Molecular Spectroscopy The free motion of molecules in the gas phase can be divided into 3 components 1) Translational 2) Vibrational & 3) Rotational

44 Translation : The motion of the molecular center of mass Rotation: The molecular motion around the center of mass while all inter-atomic distances and angles remain constant Vibration: Relative motion of atoms with respect to each other

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46 Rotational and vibrational energy levels are quantized (have specific values for a molecule) E 3 E 2 E 1 Translational motions of molecules are not quantized - no discrete spectral lines associated with this motions - no translational spectroscopy

47 Quantized energy levels - have certain, particular, discrete energy values

48 Molecular absorption processes Electronic transitions UV and visible wavelengths Molecular vibrations Thermal infrared wavelengths Molecular rotations Microwave and far-ir wavelengths ~10-18 J Increasing energy ~10-23 J Each of these processes is quantized Translational kinetic energy of molecules is unquantized

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50 Rotational spectroscopy

51 Rotational spectroscopy Pure rational spectra of molecules are caused by the interaction of molecules with microwave radiation of EMR. The range of rotational frequencies is about 8 x x Hz ~ mm - nuclear transitions between the rotational energy levels are considered

52 Dipole moment along z axis Diatomic Molecule with a oscillating dipole moment can absorb electromagnetic radiation via their rotational motion. Eg: CO, NO, and HCl

53 The rotation of a diatomic molecule is best described in terms of its angular velocity (ω), about the center of gravity of the molecule.

54 Figure goes here. A diatomic molecule can rotate around a vertical axis.. An important quantity for describing the energy of rotation is the moment of inertia( I ) m i is the mass of the atom at distance r i

55 The moment of inertial about the center of mass is From the center of mass definition

56 For a diatomic molecule

57 Rigid rotors describe the molecules that do not distort under the stress of rotation. the potential energy change may be set to zero since there is no change in bond length during the rotation. q1q2 v 4 r The energy levels obtained from solving schrödinger equation are given by: 0

58 E j energy of the J th rotational energy level/j J is the rotational quantum number I moment of inertia of the molecule/ Kgm 2 h Plank s constant /JS The constant factors, rotational constant (B), are given the symbols

59 cm -1 cm -1

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62 2B

63 Question 1: The first rotational line of CO occur at cm -1 (J=0 to J=1). Calculate the bond length of a CO molecule. h = Js c= x 10 8 ms -1 2B = cm -1 B = X 10 2 m -1

64 kgm x I m x x x x kgm x I B ms x x s Kgm x I ms x x I JS x B IC h B

65 I mr 2 I mc mo m m c o r 2 m C m O m c = 12.0X10-3 kg / x m o = 16.0X10-3 kg / x r = 1.131Ǻ

66 Question 2: The rotational spectrum of HI shows a series of lines separated by 12.8 cm -1. Calculate the inter atomic distance of HI. (H = g and I = g) Answer = 1.63 Ǻ

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68 Question 3: The first rotational line of 12 CO is occurred at cm -1 and that of 13 CO is occurred at cm -1. Calculate the mass of 13 C. Assumption: r 12 CO = r 13 CO Answer = g

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71 Rotational spectrum of non-rigid rotor High energy rotations do not obey the rigid rotor model. Because molecular bond/ inter-atomic distance is not completely fixed; the bond between the atoms stretches out as molecule rotates faster. - hence change the moment of inertia (I) - higher values of the rotational quantum numbers. - This effect can be accounted by introducing a correction factor known as the centrifugal distortion constant (D) Units of D - cm -1

72 The energy levels of the non-rigid molecule is defined as 2 4 h h 2 2 E j J ( J 1) J ( J 1) Joule 8 I 32 I r k E J energy of the J th rotational quantum level/j J is the rotational quantum number I moment of inertia of the molecule/ Kgm 2 h Plank s constant /JS r e is the equilibrium bond length/m k is force constant of the bond/ Nm -1 e j 8 h J( J 1) J ( J 1) IC 32 I re kc h cm -1

73 Simplification can be achieved by using the rotational constant (B) and defining the centrifugal distortion D. j 8 h B = h / 8π 2 IC J( J 1) J ( J 1) IC 32 I re kc ε J = E J / hc = BJ(J+1) DJ 2 (J+1) 2 cm -1 ε J is a symbol which express energy in frequency units Normally D has a value much less than B. h 4 32 I eg: HCl has B = cm -1 and D = cm -1. D is large when a bond is easily stretched D h 3 2 r e kc

74 B= h / 8π 2 IC B 1/ r 2

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