Electromagnetic Spectrum The energy of the photon determines the type of transition or interaction that occurs. Table 1-1 – Ingle and Crouch, Spectrochemical Analysis

Spectroscopy EM Radiation Sources No radiation: Excitation by collisions or chemical reactions can initiate photon emission. Continuum Source: Emit radiation over a broad wavelength range (e.g. incandescent lamps) Line Source: Emit radiation at discrete wavelengths (e.g. Hg arc lamp, laser). Image source: Tungsten Halogen Lamp Mercury Argon Lamp

Interaction between EM Radiation and the Sample absorbradiationradiationlessabsorptionemitradiationradiationlessemission emissionabsorptionphotoluminescence inelastic excitation or deactivation

Atomic vs. Molecular Spectroscopy Atomic Spectroscopy Example (Cl 2 ): Molecular Spectroscopy (CH 3 CH 2 OH): Image source:

Wavelength Selection before Detection Must separate analyte optical signal from a majority of the potentially interfering optical signals. - absorption filters - absorption filters - interference filters - interference filters - spatial dispersion - spatial dispersion - interferometry - interferometry Image source:

Are you getting the concept? The two transmission profiles below are for filters sold by Melles-Griot. Which filter would you buy to block = 15,800 cm -1 light? (a)(b)

Radiant Power Monitors (a.k.a. Detectors) Detectors convert EM radiation into an electrical signal or another physical quantity that can easily be converted into an electrical signal. Thermal Detectors: convert IR radiation into current or voltage Photon Detectors: convert UV and visible photons into current Multichannel Detectors: convert UV and visible photons into charge Skoog and Leary, Principles of Instrumental Analysis, Saunders College Publishing, Fort Worth, 1992.

EM Radiation Sources 1. Fundamentals of EM Radiation 2. Light Sources 3. Lasers

Wavefunctions (  Assume wave moves with speed v. Assume shape remains constant. y = f(x) at initial time t=0 At later time, t, the wave will have traveled a distance vt to the right. y = f(x-vt) at later time t Similarly, wave traveling to the left: y = f(x+vt)

Harmonic Waves (a.k.a. Sinusoidal or Simple Harmonic Waves) “Although the energy-carrying disturbance advances through the medium, the individual participating atoms remain in the vicinity of their equilibrium positions.” -Hecht, Optics, 2002  (x,t)| t=0 =  (x) = Asinkx amplitude in radians  (x) = Asink(x+vt) traveling in –x direction  (x) = Asink(x-vt) traveling in +x direction

Spatial Period - Harmonic Waves If this wave is traveling at speed v in the + x-direction:  (x,t) = Asink(x-vt) The wave is periodic in space and time. The spatial period is the number of length units/wave  (x,t) =  (x ±,t) With harmonic , |k | = 2  so k = 2  Usually use  to represent the argument of the sine function.  describes the phase of harmonic wave.  (x) = 0 whenever sin  = 0 (when  = 0, , etc. or x = 0, , etc.) Hecht, Figure 2.6

Temporal Period – Harmonic Waves The temporal period (  ) is the time for one wave to pass a stationary observer.  (x,t) =  (x, t ±  ) We can derive the expression:  v  v Units of  = # units of time/wave. Often use 1/  → frequency, Often use 1/  → frequency, (the # waves/unit time). Angular temporal frequency (  ) in radians/second:   Hecht, Figure 2.7

Harmonic Wavefunction Interaction Variation in the electric field for a plane-polarized wave: E = E m sin (  t +  ) When two wavefunctions interact, consider the similarity or difference in: *amplitude (E m ) *frequency (  ) *phase (  ) How do these characteristics influence the electric field resulting from wavefunction interaction?

Are you getting the concept? Sketch the sum wavefunction of the red and blue waves. 

If  1   2, the phase changes: Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

Superposition Principle Figure 3-4 – Ingle and Crouch, Spectrochemical Analysis Constructive Interference: If two plane-polarized waves overlap in space, the resulting electromagnetic disturbance is the algebraic sum of the two waves. Destructive Interference: The interaction of two or more light waves yielding an irradiance that is not equal to the sum of the irradiances.

Optical Interference Constructive Interference  2 –  1 =  =  m 2  where m is an integer Destructive Interference  2 –  1 =  = (2m+1)  where m is an integer Figure 3-4 – Ingle and Crouch, Spectrochemical Analysis

Electromagnetic Radiation Seminal work by: Faraday, Gauss, Ampère, and Maxwell A time-varying electric field has an associated magnetic field. A time-varying magnetic field has an associated electric field. The electric field due to point charges. A closed surface in a magnetic field has a net flux of zero. Implies a mathematical and physical symmetry between electric and magnetic fields.

Electromagnetic Radiation Consider: - the general perpendicular relationship between E and B - the general perpendicular relationship between E and B - the symmetry of Maxwell’s Equations - the symmetry of Maxwell’s Equations - the interdependence of E and B - the interdependence of E and B Use Maxwell’s Equations to calculate the speed of EM radiation in free space: c = x 10 8 m/sec Skoog and Leary, Principles of Instrumental Analysis, E x B points in propagation direction Moment-to-moment direction of E is the polarization

Energy and Momentum EM waves transport energy and momentum. The energy streaming through space in the form of an EM wave is shared equally between the electric and magnetic fields. Irradiance (I) quantifies the amount of light illuminating a surface. I =  0 c r The irradiance from a point source  1/r 2 The time rate of flow of radiant energy = optical power (P) measured in watts r

Photon Force When an EM wave impinges on a material, it interacts with the charges that constitute bulk matter. It exerts a force on that material. (Newton’s 2 nd Law suggest that waves carry momentum.) Maxwell wrote, “In a medium in which waves are propagated, there is a pressure in the direction normal to the waves, and numerically equal to the energy in a unit of volume.” The radiation pressure ( P ) is the energy density of the EM wave. Assume that the E and B fields are varying rapidly, calculate the average radiation pressure: T = I/c (units = N/m 2 ) T = I/c (units = N/m 2 )

Are you getting the concept? If the average irradiance from the Sun impinging normally on a surface just outside the Earth’s atmosphere is 1400 W/m 2, what is the resulting pressure (assuming complete absorption)? How does this pressure compare with atmospheric pressure (~ 10 5 N/m 2 )?

Photon Emission E. Hecht, Optics, atom in ground stateatom in ground state atom excited by high T or collision, stays in excited quantum state for or secatom excited by high T or collision, stays in excited quantum state for or sec atom returns to ground state, emitting a photonatom returns to ground state, emitting a photon Frequency of emitted light is associated with the quantized atomic transition (  E = h )

Photon Radiation Figure 5-16 Partial energy-level diagram for a fluorescent organic molecule. Skoog and Leary, Principles of Instrumental Analysis, 1992.

Are you getting the concept? Many streetlights are sodium discharge lamps. The emitted orange light is due to the sodium D-line transition: What is the energy level spacing (in eV) for the 3p → 3s transition?