Diffraction & Spectroscopy PDF

# Diffraction & Spectroscopy ## Page 1 **E** **Dittraction & Spectroscopy** **E** **↑** **K** **K** Semiconductor hydrogen Spectroscopy: Area where we study spectrum - plot of intensity / Amplitude Vs. E/ω/π/λ. **I/A** **→ Elw/ila** **→ Energy level Piagrani** one to one mapping. Soli...

# Diffraction & Spectroscopy ## Page 1 **E** **Dittraction & Spectroscopy** **E** **↑** **K** **K** Semiconductor hydrogen Spectroscopy: Area where we study spectrum - plot of intensity / Amplitude Vs. E/ω/π/λ. **I/A** **→ Elw/ila** **→ Energy level Piagrani** one to one mapping. Solids, liquids & Gases. ## Diffraction: X-ray diffraction, electron diffraction Bragg's lave: ηλ=2dSino. Construtive & distrutive patterns - crystal stricture. Solids, liquids. Types of ice: Amorphous, crystalline ice → Depends on rate of cooling. Electromagnetic waves consists of Oscillating electric and magnetic field. A changing electric field produces a changing magnetic field. ## Page 2 thats houи will change electric fields and magnetic fields Oand electromagnetic wave to be generated. [Accelerated charges create electromagnetic waves] ## Properties of electromagnetic waves. → Amplitude - maximum strength of the Em wave. → Points a & b are in phase to each other → Points c & d are not in phase to each other. → frequency = No of waves Hz → Speed of the wave = fλ. → Any electromagnetic wave in vacuum will have a constant speed. 3x108m/sec. (independent of f & λ) → EM waves differ in frequencies. ## Electromagnetic wave equations in free space wave equation in Em wave: As per Faraday's law. DXE = - dB / dt Take curl on Both sides. XOXE = -d (DXB) / dt ▽(DE) -D2E = d(DXB) / dt → ① →As per Gauss lave of electric field. V.D = Sv V.(EE) = Sv → for free space Sv = 0 VE = Sv D.E = 0 eq2E = d(DXB) / dt = μο2(XH) / dt ## Page 3 As per Ampure clicut lave for time varying field. √x H = J + 2D / dt → conduction current density For free space J=0VXH = 2D / dt = E02E / dt from above equation eq② ΖΕ = μοεο 22Ε / atz For free space, C = √1 / μοεο 22E / c272E = DZE / atz → Wave equation 1 / c2 * ∂2E / ∂tz = 2 (propagation constant) ∂2E / ∂tz = 7²E → Wave equation ## Spectroscopy functional form of wave E = EoEi(-k ᵪ - ωt) → frequency Re(e) → wave vector 2 → Electric field EM πw=Hoe(kᵪ - ωt) plene wave HIELR ## UV-Vis spectra Solids liquids Gases } molecules or atoms Y Bonding Y spatiation Final Bend Structures. ## Page 4 **E** **n:2** **photon** **→phonon.** > **→elactic proces.** **n=1 (Ground)** é recombining at different energy state > **Inclactic procus** cone (fourier space) is inelaitic prown. * Elastic & inelactic process is w.r.t emission & not absorption. - αιχ Concentration I=e-αχ length Io Io → I Aurage = absorption per unit length per unit concentration At t = 0 E=Exxei(kz) K² / λ = 2πη n = nrtini E=Ex.nle^(2πηί / λ) e^(-αχ) = e^(-αχ) 2/ ΛΕ ni, a n = f (E) D(E) de. Ec 1M = 1 mol / l. 1 mole= 6x10^23 molecules le. ## Page 5 35mm Back word Scatter -ing. Forward Scattering Extinction = Absorption + Scattering. ## Scattering of a dipole ## UV spectroscopy absorption 30m 0 Bopfr 40nm λ ←→ **DS** Shift of peak based on particle Bize → peale stronger Localized surface plasmon corresponding to length resonance? ## Page 6 Sai Ram Krishna Sir : Axes of spectra in UV-Vis Intensity Vs λ, Ε(ΔΕ) UV VIBGYOR IR 400nm 700mm Intrared→ creuse heating Infrared 3700 λ. υν λ < 400nm (Bends less) high energy. E = hc / λ Inelastic process → Scattering. Intensity → Blue Shift CCD - charged coupled device (peak Shifting towards left) red shift (peak changing towards Right) 300nm. 700nm of Em radiation. Intensity can be quantified using Prism. Spectroscopy → Inelastic scattering event is associated with energy loss and this energy loss (mavelength) can be quantified. Energy quantification. Electron loss spectroscopy → Sputroscopy using energy loss X-ray photo emission spectroscopy. photon emission is quantified to study the spectroscopy of the material. of electrons with matter. Optical spectroscopy & Electron energy loss spectroscopy are closely related. Back scattered incident-high e- EDX Kv beam → →Augere- Le visible light (Cathedo Luminiscence! e-hole pair Characteristic x-rays (Energy dispersive Spectroscopy of x-rays) Absorbed Inelastically Scattered e- (Electron energy loss Spectroscopy, e Direct beam ECLS) → Bremstrahlung x-ray's. Mastically scattered e- ## Page 7 →All the above are inelastic processes. Fluroscence → Emission of light is spontaneous (400-6000m) phosphorescence → Emission of light is not spontaneous. → Energy of emission within the optical energy → we get visible light. Signals in EELS Angle of incident beam & anger of diffrailed beam can be related using Rutherford's relation. Scattering cross ection Diffraction grating ← ↑y Asino-ma ye MAD a y = 15cm EDS → Energy dispersive spectroscopy Cathedo luuminscence D=100cm a = ? λ = e 7hr (Cathedo luminiscend) EELS Raman Spectroscopy Raman →inelactic scattering process. Ei → Gole photon energy ↳ input photon energy ~ hr= Eo Virtual Energy level E01 Goz Eo3 ## Page 8 E03 = Ei→ Rayleigh scattering Eoi > Ei → Anti stokes Eo2. <Ei→ Stokes. I Antistokes Stokes. rayleigh J= 7=1/λ ㅗ = Reference Laser λ (cm²) output 7=0 Rayligh scattering. Y=tve → stokes =-ve → antistokes E= hc/ λ △E=hc(1/ λ1 - 1/ λ2) Why is Raman so special? How does Raman tells us bond vibrations 7 CV Raman's Experiment Sunlight Violet Scattering liquid.. Violet Mipeter Rayleighs Scatter Ranmans scatter Violet Green green filter Green Y Observer. ## Page 9 Why intensities of Stokes stronger than antistokes? intensity & Number of photons per energy level per unit time. Stokes X Temperature. Antistokes @what is the Raman shift? What determines the intensities of the peaks? *** Gas lasers has extremly norrow..... 7 Tuo Raman experiments one for E1 = 532mm E2=623nm G2 GT Intensity E1 (532nm) E2 (623 nm) 2) position remains same intensities can vary Raman is 1000 times weaker than fluroscence which is 1000 times weaker than incident light. Ans: →Bonds in the molecule → Sample quality. →Instrumentation - detector, source, officiency etc. CCD. Mathematical basis of Raman scattering. Different Raman Bands →Finger print method. ## Page 10 # Diffraction and Spectroscopy ## UV-Vis spectroscopy →Source UV rays or Visible light (200nm to 800nm) frequency & Energy frequency a 1 Tray x-ray frequency 1 Energy Wavelength & Wavelength UV Vis 200nm 400nm 200 nm to 400non υν range 400nm to 800nm → Visible range micro IR 800nm 1 Beam monochromater seperator Control Chamber Glass → Cuvette (H20) Prism light source Detector Sumple chamber Sample Monochromatic light → Whenever a specific wavelength of light hits a molecule, that molecule gels excited and the electron once excited fimeps up from ground State to higher energy state & that particular light energy is absorbed. → The light passing through the glass cuvette containing water is almost of the same energy indicating that there is no light/Energy absorbed by H20 molecules. → Initially sample is also H2O → Io = I → Example solution = proteins absorbs a specific wavelength of light more protein concentration → more absorption → lesser intensity of light detected. Net change in intensity IT = I-IO Transmittance T= I/ェ。 ## Page 11 more transmittanu→ less absorption % transmittanu Concentration Molecular level mechanism : C-C C=0 *ドー م - (Conuntration x length) T= 10 Absorbance = Excone x length Conc = A El. C-C o bond C=ㅇㅈ bond * high energy state éé n K e - ground state → For excitation, e rely on a specific wavelength → if wavelength of light is shorter (high frequency, high energy) for a O bond then e will jump from o orbital to o* orbital ## Elastic and Inelastic process. V n=2 * Elactic proves & inelastic proces depends on emission and not absorbtion. -१८x n=1 (ground state) * I-e- = I / Io I Inelartic process Elastic process → Average = absorbtion per unit length per unit concentration C concentration xlength ## Page 12 Note: E = hr = hc / λ h=6.626x10^-34g5 C = 3x 10° on /sec. Watt = Joules/sec NA = 6.022x10^23 Calculate the energy of one mole photons of wavelength of 600 nm E=hc= (6.626x10^-34) (3x10^8) / (600x10^-9) = 3.313x10^-19 J EXNAV = 3.313x10^-19 x 6.022x10^23 ENAN = 199.5 KJ. consider an LED bulb with arage wavelength λ=600nm efficeincy is 100% If Energy of one mole of photon is 199.5KJ and Power of bulb = 5w then how long will it take to create one mole of photons Watts = Joules / Sec photons created in one hour → Joules = 5x3600 = 18 KJ Photons hour 18 KJ 1hr 199.5 11hr 18 199.5KJ ## What is Spectroscopy? Spectroscopy is defined as the interaction between light and matter hight → electromagnetic wave which oscillates in space. Wavelength Amplitude distance→ V= frequency A = wavelength Velocity = wavelength x frequency → when light is passed through a prism then the components of light are arranged in the order of the swavelengths ## Page 13 The prouss of getting the spectrum is called sфитохору Note: Solar spectrum → Solar Spectrum consists of many dark lines Fraunhofer lines ↓ used to find out various servers, in the solar atmosphere Flame test: Nail → bright yellow → ↓ Ballz → green Liel → red Culle → blue Types of spectroscopy emission Spectroscopy ← Absorption Spectroscopylight absorbed by matter Light-matter Interaction. Light ← light → manes particle nature |- → construtive es emitted by Matter → districtive interference Wave Note: 1 quanta of light has the energy E = hr Nail → flametest ↓ flemetest Yellow light emitted ↓ enmission spectroscopy > photoelectric effect h = planks constant.. h = 6.626x10^34 Js compton scattering λ initial wavelength 12 scattered wavelength of x-ray X-ray E= hr = hc λ. →when there is a change in the wavelength then there is a corresponding change in the energy ## Page 14 The prouss of getting the spectrum is called spectroscopy Note: Solar spectrum Solar spectrum consists of many dark lines Fraunhofer lines ↓ used to find out various elements in the solar atmosphere Flame test: Nacl → bright yellow. Ballz → green Lice→red Culle → blue Types of spectroscopy Absorption Spectroscopylight absorbed by matter emission. Spectroscopy ← Light-matter Interaction Light ← light → manes particle nature |- → construtive es emitted by matter → districtive interference Wave Note: 1 quanta of light has the energy E = hr Nail →flametest ↓ flemetest Yellow light emitted ↓ enmission spectroscopy. >photoelectric effect h = planks constant.. h = 6.626x10^34 Js compton scattering λ initial wauwlength 12 scattered wavelength of x-ray X-ray E= hr = hc λ. →when there is a change in the wavelength then there & a corresponding change in the energy ## Page 15 Bohr: When light interacts with hydrogen atom, electron jumps from one stationary state to another stationory state n=3 7=2 Ei lEf-Eil= hr n=1 ΔΕ=hr Bohrr's condition. Ef ΔΕ=hr +Ze Bohr model →Einstein postulated that the rate of absorption of light by matter is proportional to the radiant energy density of light with the right frequency Total radiant energy density (light has many frequencies) S= kilri) + kzl72) + ka (rs)... 11, 12, 13 different SJ/m3 71, 72, 7s frequencies of light ds = 8,71 dri -3 ->Energy density at a certain frequency Sr = ds Jsm³ Ef > Ei→ absorption Ef < Ei emission ## Types of emission →Stimulated Emission light stimulates the emission process Spontaneous emission Atoms/molecules in a higher energy state Can come down Spontaneously to a couия energy statt Ez E₁ ground state ## Page 16 # Raman Spectroscopy →Raman effect is a light scattering phenomena on matter, it may be absorbed it the energy → when light falls of the radiation corresponds to the superation of levels of the matter (atoms/molecules) the two energy →If absorption does not takes place, the electromagnetic radiation is either transmitted or scattered. →Raman spectroscopy is related to this scattering of light. → whereas rotational spectroscopy, virrational spectroscopy and electronic spectroscopy involves absorption is encussion of light. Scattered light (Is, λ) or (Ις, λ') Incident light. (Io, 7) Matter →Transmitted light (Ιτ, λ) Is, λ → Rayleigh Scattering -4 Ιδαλ + 2 explains blue color of the sky → Raman scattering. Is, λ' Optical analog Compton yfect Raman effet Raman's esperimental setup. λ (IT) Transmitted light Bunlight Monochromater Samples Scattered filter light (Is) removes A Scattered light at any other wavelength Other than the incident wavelength detector (eye) ## Page 17 1 Classical theory of Raman effect →when an EM wave is incident on a matter, the e orbits within the constituent molecules are perturbed periodically with the same frequency as that of the electric field of the incident wave. →The oscillation or perturbation of the ecloud results in a periodic seperation of charge within the molecules and this is called the induced dipole moment. →Electric field induces a dipole moment in the molecule. →This oscillating dipole moment is manifested as a source of EM radiation and thereby resulting in scattered light. →The majority of light is scattered in the identical frequency (Vo) of the Incident light and this process is referred as cleartic scattering. →Raman scattering is an example of Inelastic scattering. Induced dipole moment Mind = αΕ d→ polarizability (distortion of molecule) Electric field of the incident EM wave ⇒ E = Eocos(wot) Mind = αE Wo=2xYo Yo = C Eo → Amplitude λο Yo frequency of incident light Mind = a Eo Cos(2万rot) ① The physical displacement (28) of the atoms about their equilibrium position due to a periodic motion (rotation or vibration) dQ = Qo cos(2xYmt) Im frequency of matter So → maximum displacement about equilibrium position Approximation → Taylor series expansion d = do + da lelog '. x = do da Qocos (2xYmt)→② dos legha do ## Page 18 from @f@ Mind = [ do + da / dg Qocos (2xYmt)] [Eocos (2x-rot)] COSA COSB = 1/2 [COS(A+B) + COS(A - B)] ⇒Mind = loEo Cos(2xYot) + (da / dg Q900) [cos(2x (To-rm) t) + Cos(2x (tot/m) QoEo 2. incident frequency :: Elastic scattering (or) Rayleigh scattering Raman scattering Inclastic scattering Stokes scattering Antistokes Scattering →Shorter →Longer wavelength up shifted down shifted fraquincy frequency. Necessary condition for Raman scattering da≠0 dg