1801 Fundamentals of Spectrophotometry

Electromagnetic Radiation

Validation of Theory of photons concept Theory of Equation for Theory of Dual nature of quantum energy and explanation of electromagnetic wavelengths of lines quantum energy Particle/wave duality electrons and photons photoelectric radiation in visible spectra and photons effect of electrons proposed demonstrated

1864 1885 1890 1892 1900 1902 1905 1913 1925 1926 1927

Formula for Proof of Theory of Bohr developed Establishment of hydrogen spectrum electromagnetic electron “shells” model of hydrogen Heisenberg’s determined radiation atom uncertainty principle. Wave equations. Unification of quantum theory and wave Problem Set Chp17: mechanics.

1 Fundamentals of Spectroscopy Aug ‘17 Nature of Light (Electromagnetic Radiation)

What is light? What are its component? What is the difference between red light and blue light? How do scientist use radiation to probe matter.

2 Fundamentals of Spectroscopy Aug ‘17 Electro- Magnetic- components of light

Light is a form of energy that can be describe as a wave l - wavelength, length of a wave from crest to crest or trough to trough (nm) n (nu)- the number of waves (cycles) which passes a given point (Hz or s-1 )

freq.(n) µ 1/ l larger n, smaller l n = c / l ® nl = c

c - speed of light, 3.0•108 m /s in vacuum

3 Fundamentals of Spectroscopy Aug ‘17 The Electro- and Magnetic- of light

Electromagnetic Radiation Light has an electrical component Light has a magnetic component. All electromagnetic radiation has fundamental properties and behaves in predictable ways according to the basics of wave theory. Electromagnetic radiation consists of an electrical field(E) which varies in magnitude in a direction perpendicular to the direction in which the radiation is traveling, and a magnetic field (M) oriented at right angles to the electrical field. Both these fields travel at the speed of light (c).

4 Fundamentals of Spectroscopy Aug ‘17 Light - Electromagnetic Spectrum

Visible light is actually superposition of different colors. Colors of light is due to EMR’s different wavelength or frequency

5 Fundamentals of Spectroscopy Aug ‘17 Electromagnetic Spectrum

EMR Spectrum Visible light is one component of a gambit of radiation.

Electromagnetic spectrum Visible light (enlarged portion) is but a small part of the entire spectrum. The radiation’s energy increases from the radio wave end of the spectrum (low frequency, n and The solar spectrum long wavelength, l) to the g-ray and (high frequency and short wavelength).

6 Fundamentals of Spectroscopy Aug ‘17 Frequency -Wavelength Relationship E= hn = hc/l, c = 3•108 m/s , 1•107 nm=1 cm, h = .63•10-34 J/s

Calculate the frequency of red light given l = 700nm: n = c/l Red light - l = 700 nm ~ 700•10-9 m n = 3•108 m/s / 700•10-9 m = 4.28 • 1014 s-1 n = 4.28 •1014 Hz

Calculate the wavelength of 92.5 MHz (91.X FM): l = c/n l = c / n = 3•108 m / s • 1 / 92.5 •106 Hz l = 3.24 m

Calculate the wavenumber n for UV light 300 nm n = 1/l = 1/300nm • (1•107nm/1cm) = 33333 cm-1 (1•107/ __nm) g cm-1

7 Fundamentals of Spectroscopy Aug ‘17 Higgs-Boson Particle

The "God particle" is the nickname of a subatomic particle called the Higgs boson. The Higgs boson, or “God particle,” is believed to be the particle which gives mass to matter. The “God particle” nickname grew out of the long, drawn- out struggles of physicists to find this elusive piece of the cosmic puzzle.

The Higgs boson is often referred to as the "God particle" by individuals outside the scientific community, after the title of Leon Lederman's book on particle physics, The God Particle: If the Universe is the Answer, What Is the Question? Lederman said he gave it a nickname because the particle is "so central to the state of physics today, so crucial to our understanding of the structure of matter, yet so elusive,” and added that he chose "the God particle" because "the publisher wouldn't let us call it the Goddamn Particle, though that might be a more appropriate title, given its villainous nature and the expense it is causing.”

8 Fundamentals of Spectroscopy Aug ‘17 Particle -Wave Duality

Planck - Einstein : Energy possesses Mass

E = hυ Light: Wave or Particle ? 1 2 E = 2 mc 1 2 Wave hυ = 2 mc hc = 1 mc2 Particle λ 2 2hc 2 = m c λ 2hc Photons m = c2λ

Light has Mass Footnote: • This particle-wave duality bothered Einstein so much he tried to develop a “Unified Model” .... to his death. • Recently String Theory has been developed to explain the behavior of matter and energy in more detailed.

9 Fundamentals of Spectroscopy Aug ‘17 Wave Property of Electrons

Louis DeBroglie (1923), Sorbonne, Paris. pH.D. Thesis Particle-Wave Duality

If energy (radiation) behaves like a stream of particles, then could matter (under appropriate conditions) show wave-like properties

Indeed, light possesses momentum which can be measured by pressure of light exerted on object.

E p = mu p = Where c U-velocity p-momentum E mu = c hν h u = n l mν = mu = c λ

muc h ν = λ = h mu

-1 ν ∝m λ ∝m

10 Fundamentals of Spectroscopy Aug ‘17

€ Matter Possesses Wave

Electron diffracted by NaCl crystal. Diffraction is a property of light that is easily interpreted by using wave model.

Experiment confirms DeBroglie’s equation

DeBroglie’s Explanation

• Electron behave as standing or stationary wave

• The circumference of Bohr orbit must be a whole number which is a whole number multiple of the electron’s wavelength.

11 Fundamentals of Spectroscopy Aug ‘17 Wave Vs. Particle

Photon Electrons (Planck’s) (DeBroglie)

Energy: 1 2 E = hν E = 2 mu hc h Wavelength λ = λ = E mu

1 Velocity 8 m 2E 2 c = 3 • 10 s u = [ m ]

E = hn = h c / l = h c n , 1 ev = 1.60 •10-19 J

12 Fundamentals of Spectroscopy Aug ‘17 Color and Perception

400 500 600 800

The relationship between Colors and Metal Complexes

13 Fundamentals of Spectroscopy Aug ‘17 Colors & How We Perceive it

Artist color wheel showing the colors which are complementary to one another and the wavelength range of each color.

14 Fundamentals of Spectroscopy Aug ‘17 The color of Visible light

15 Fundamentals of Spectroscopy Aug ‘17 Black & White

When a sample absorbs light, what we see is the sum of the remaining colors that strikes our eyes.

If a sample absorbs all wavelength If the sample absorbs no of visible light, none reaches our visible light, it is white eyes from that sample. or colorless. Consequently, it appears black.

16 Fundamentals of Spectroscopy Aug ‘17 Absorption and Reflection

If the sample absorbs all but orange, the sample appears orange.

Further, we also perceive orange color when visible light of all colors except blue strikes our eyes. In a complementary fashion, if the sample absorbed only orange, it would appear blue; blue and orange are said to be complementary colors.

17 Fundamentals of Spectroscopy Aug ‘17 Complex Influence on Color

Factors Affecting Color The metal Oxidation state Partially filled d-orbitals (d0 and d10 transparent)

Solutions of common transition metal compounds showing various colors.

18 Fundamentals of Spectroscopy Aug ‘17 How we perceive colors

The Visible Spectrum Wavelength Region Color of Light Complementary Color Absorbed, nm Absorbed Transmitted (what we see) 400-435 Violet Yellow-green 435-480 Blue Yellow-orange 480-490 Blue-green Orange 490-500 Green Red 500-560 Green-yellow Violet 560-580 Yellow-green Purple 580-595 Yellow-orange Blue 595-650 Orange Blue-green 650-750 Red Green

A solution of FeSCN2+ is not red because the complex add red radiation to the solvent.

19 Fundamentals of Spectroscopy Aug ‘17 The color of Visible light

Light is a form of energy carried by electric and magnetic fields traveling at 186,000 miles per second. Light has both particle and wave characteristics. The wavelength determines both its color and its energy; the shorter the wavelength, the higher the energy. Light or electromagnetic radiation, ranges from gamma rays (10-15 nm) through the visible region (500 nm) to the radio wave region (100 m). In the visible region, white light contains a spectrum of wavelengths from 400 nm (violet) to 780 nm (red); these can be seen in a rainbow or when light passes through a prism. The color of substances depends on the color of light absorbed by the molecules or atoms that compose the substance. This, in turn, depends on the energy separations between electron orbits. When a molecule or atom absorbs light, electrons are excited from lower energy orbits to higher energy orbits. If the energy of the light is high enough, light can break chemical bonds and destroy or change molecules through photo-decomposition; usually, however, the energy is simply given off again as heat or light through relaxation. The specific wavelengths at which molecules or atoms absorb or emit light serve as fingerprints for specific substances, making spectroscopy—the interaction of light and matter—a useful tool in identifying unknown substances. Magnetic resonance imaging and laser devices are two important applications of light and its interaction with matter. Light is a fundamental part of our lives as it is responsible for what we see. Sunlight is what keeps the earth alive and is our ultimate energy source. Human eyes can see a narrow band of light called visible light, but humans use many other wave-lengths for various purposes: X-rays and gamma rays are used in medicine, infrared light is used in night vision technology, microwaves are used in cooking, and radio waves are used in communication. The human eye evolved to see not only different intensities of light (black and white vision) but different colors as well. The colors that we see depend on the interaction of light with the molecules or atoms within the thing that we see.

20 Fundamentals of Spectroscopy Aug ‘17 The incandescent Bulb

An incandescent bulb will emit radiation at all wavelength much like a black body radiator.

21 Fundamentals of Spectroscopy Aug ‘17 Interaction of Radiation with Matter

The region of the electromagnetic spectrum. Interaction of an analyte with electromagnetic radiation can result in the types of changes shown. Note the changes in electron distributions occur in the UV/Vis region. The wavenumbers, wavelength, frequency and energy are characteristics that describes electromagnetic radiation.

22 Fundamentals of Spectroscopy Aug ‘17 Spectroscopic Measurements

The interaction of radiation with matter provides information about the sample. The sample begins at its ground state, absorbs the radiation and is stimulated to its excited state. The radiation that is absorb (ground state to excited state) or emitted (excited state returns to its ground state) contains the information. In the example below, the analyte is stimulated by nonradiative process such as heat, electrical energy or chemical reactions.

Absorption of energy (thermal, electrical or chemical Energy)

Chemiluminescence - excitation from a chemical reaction.

Emission - heat or electrical energy

23 Fundamentals of Spectroscopy Aug ‘17 Type of Spectroscopy

Absorption - radiation is absorb

photoluminescence - emitted photons after absorption fluorescence is the instantaneous emission phosphorescence is the delayed emission

24 Fundamentals of Spectroscopy Aug ‘17 H-Line Spectrum

Hydrogen Line Spectrum: When hydrogen gas (or other element) receive high energy spark it emits light with specific l -wavelength signature

H2 (g) absorb energy (H-H bond breaks) ® H atoms H-atoms are excited to higher energies. These atoms discard excess

energy by giving off EMR; then combine to form H2 molecules again.

H* H H* Excited hν H State H* H hν hν

25 Fundamentals of Spectroscopy Aug ‘17 Bohr Model Illustrated • Electron orbits in circular orbit around proton in permitted allowed orbits. (This is so that electrons won’t spiral down toward nucleus). • Electrons can change to another allowed orbit e- jumps to an energy level (absorbs energy) e- relaxes down (emit energy) hv

e e e e hv

ground state excited relaxation pathway ground state state In the process of absorbing energy In the relaxation process, since (or photons) the electron of H is energy is conserve, energy is release promoted to a higher orbital. in the form of light (photons, hv).

26 Fundamentals of Spectroscopy Aug ‘17 Bohr Model of the H-atom Model of the Hydrogen atom / Atomic line Spectrum

8 ... ∞ 7 8 ∞ 6 7 56 5 What is the origin of 4 4 3 3 Pashen: n = 3 the Atomic Line 2 f 2 spectrum ? Balmer: n f=2 1 Lyman: n f = 1 1 P

Lyman: n f = 1 Pashen: n f = 3

Balmer: n f=2

Lyman: n f = 1 Balmer: n f=2 Pashen: n f = 3

Electromagnetic Spectrum 100 nm 400 nm 600 nm 1000 nm 1400 nm

Lyman: Balmer: Paschen: λ = 95.0 nm (5-1) λ = 410 nm (6-2) λ = 1005 nm (7-3) 97.3 nm (4-1) 434 nm (5-2) 1094 nm (6-3) 102.6 nm (3-1) 486 nm (4-2) 1282 nm (5-3) 121.6 nm (2-1) 656 nm (3-2) 1875 nm (4-3)

27 Fundamentals of Spectroscopy Aug ‘17 Pathways to Relaxation

Different illustrating of e- relaxing back to ground state.

1. Atomic shell diagram Model of the Hydrogen atom / Atomic line Spectrum

8 ... ∞ 7 8 ∞ 6 7 56 5 4 4 3 3 Pashen: n = 3 2 f 2 Balmer: n f=2 2. Energy Level Diagram n=¥ 1 ∞ Lyman: n = 1 8 1 f 7 P 6

Lyman: n f = 1 5 Pashen: n f = 3 4

Balmer: n f=2 3

Lyman: n f = 1 Balmer: n f=2 Pashen: n f = 3

Electromagnetic Spectrum 1 100 nm 400 nm 600 nm 1000 nm 1400 nm

Lyman: Balmer: Paschen: 3. Step Analogy 4. Well λ = 95.0 nm (5-1) λ = 410 nm (6-2) λ = 1005 nm (7-3) 97.3 nm (4-1) 434 nm (5-2) 1094 nm (6-3) 102.6 nm (3-1) 486 nm (4-2) 1282 nm (5-3) 121.6 nm (2-1) 656 nm (3-2) 1875 nm (4-3)

28 Fundamentals of Spectroscopy Aug ‘17 Atomic Line Spectrum (2)

The emission Lines for various atom (EMR line spectrum) results from the relaxation process of the electron from a higher excited state orbital to a lower ground state. The Rydberg equation is able to calculate the line spectrum due to this process for the H-atom. Unfortunately this equation only works for the Hydrogen and Hydrogen-like (species with only one electron) because Bohr model of the atom breaks down when there are more than two electrons. Quantum Mechanics was developed to determine the energy of the electron due to electron-electron repulsion which was the shortcoming of the Bohr model. This theory lead to the Schrodinger equation which provide a mathematical model of the atom and its electronic behavior: HY = EY.

Line emission spectra of hydrogen, mercury and neon. Excited gaseous elements produce characteristic spectra that can be used to identify the element as well as determine how much element is present in a sample.

29 Fundamentals of Spectroscopy Aug ‘17 Radiation Absorption Absorption Process is best described by Beer-Lambert Law

Attenuation (decrease of photon to sample) of a bean of radiation by an absorbing solution. The incoming radiation has a higher radiant power than the radiant transmitted by the solution. The path length of the absorbing solution is b and the concentration is c.

A = -log T

= log (Po/P)

= e b c

c = molarity (M) e = molar absorptivity L mol-1 cm-1

Optimal A: 0.4 - 0.9

30 Fundamentals of Spectroscopy Aug ‘17 Reflection and Scattering Loss

Radiation and scattering losses with a solution contained in a typical glass cell. Losses by reflection can occur at all the boundaries that separate the different material.

To correct against such error, the power of the radiation transmitted through the sample is compared to the radiation that passes through an identical cell that contains only the solvent or reagent blank.

Light Attenuation:

Absorbing loss Scattering loss Reflection loss

When glass cell contains water, 8.5 % of the yellow light is lost due to reflection. Other cause of scattering is due to dust or particle size of analyte.

31 Fundamentals of Spectroscopy Aug ‘17 Terms in Absorption Recommended terms approved by the American Chemical Society

32 Fundamentals of Spectroscopy Aug ‘17 Beer’s Law There are several ways in which the law can be expressed, A= a b c

-A -abc P1 / Po = 10 = 10 where, A = log10 (I0/I1) a = 4pe / l

* A - absorbance * P Power intensity of incident light o P1 * P1 Power intensity of light passing through the material P * b is the distance that the light travels through the material (the path length) 0 * c is the concentration of absorbing species in the material * a is the absorption coefficient or the molar absorptivity of the absorber bb * l is the wavelength of the light * e is the extinction coefficient

The law states that there is a logarithmic dependence between the transmission of light through a substance and the concentration of the substance, and also between the transmission and the length of material that the light travels through. Given b and a the concentration of a substance can be deduced from the amount of light transmitted by it.

If the material is a liquid, it is usually express as the absorber concentration via mole fraction i.e. a dimensionless fraction. The units of the absorption coefficient are thus reciprocal length (e.g. cm−1). If the concentration is expressed in moles per unit volume, a, is a molar absorptivity (usually given the symbol ε) in units of mol−1 cm−2 or sometimes L·mol−1·cm−1.

In the case of a gas, the concentration may be expressed as a number density (e.g. cm−3), in which case a, is an absorption cross-section and has units of area (e.g. cm2).

The value of the absorption coefficient a, varies between different absorbing materials and wavelength for a particular material. This value is determine by experiment.

33 Fundamentals of Spectroscopy Aug ‘17 Using Beer’s Law

Beer’s Law can be used to calculate molar absorptivities of species given the concentration, absorbance and the path length

Typical absorption spectra of potassium permanganate at five different concentration. The concentrations are given as ppm of Mn. A plot of absorbance at the peak wavelength at 525 nm vs. concentration shows Beer’s Law behavior.

34 Fundamentals of Spectroscopy Aug ‘17 Limits to Beer’s Law

Spectrometer most accurate at intermediate levels of absorbance A~ .4 - .9

Beer’s Law many not always be obeyed. Deviation from Beer’s Law may be real deviation, instrumental deviation or chemical deviation.

Real Deviation - Beer’s Law applies only to absorption behavior under dilute solutions < 0.01M. This is the Limiting Law. At concentrations higher than 0.01M, the average distance diminish between ions causing alteration of the electrostatic interactions and the departure of Beer’s Law.

Chemical Deviation - Under some conditions, absorbing species undergoes association, dissociation, or reaction with solvent to give products that have different absorption features from the expected product.

Instrumental Deviation - Deviation from Beer’s Law result if i) polychromatic radiation rather than monochromatic radiation is used ii) the stray light contaminates the sample (close sample chamber) iii) mismatch cells are used. iv) error in alignment of cell v) dust producing scattering of light. vi) no smudge or finger print on cuvettes.

35 Fundamentals of Spectroscopy Aug ‘17 Absorption Spectra Absorption spectroscopy refers to a range of techniques employing the interaction of electromagnetic radiation with matter. In absorption spectroscopy, the intensity of a light’s beam is measured before and after interaction with a sample is compared. Light that is attenuated from the sample toward a detector on the opposite side of the sample is said to be detected in transmission and treated according to the theory of transmission spectroscopy. Light that is attenuated from the sample toward a detector on the same side (or right angles) of the sample is said to be detected in emission and it is this light that is the subject of emission spectroscopy. The remitted radiation may be composed of two kinds of radiation referred to as specular reflection (when the angle of reflection is equal to the angle of incidence) and diffuse reflection (at all other angles).

36 Fundamentals of Spectroscopy Aug ‘17 Modes of Spectroscopy

Different set up for spectroscopy

37 Fundamentals of Spectroscopy Aug ‘17 Absorption Spectroscopy Molecules undergo three type of transitions that covers ultraviolet-visible, infrared, and microwave radiation. Infrared promotes vibration of the molecule and microwave stimulates rotation of the molecule. Ultraviolet-visible radiation results in the promotion of an electron to a higher energy level. X-rays and high energy UV ruptures chemical bonds.

Energy-level diagram showing some of the energy changes that occur during absorption of infrared (IR), visible (VIS), and ultraviolet (UV) radiation by a molecular species.

The length of the transition in the diagram relates to the energy of the transition. The total energy, E associated with a molecule is given by:

E = Eelectronic + Evibrational + Erotational

38 Fundamentals of Spectroscopy Aug ‘17 Transitions and Excitations

An excited molecule can possess any one of a set of discrete amounts (quanta) of energy described by the laws of quantum mechanics. These amounts are called the "energy levels" of the molecule. In UV/VIS spectrophotometry, the major energy levels are determined primarily by the possible spatial distributions of the electrons and are called electronic energy levels, and to a lesser extent by vibrational energy levels, which arise from the various modes of vibration of the molecule (e.g. the stretching and bending of various covalent bonds).

For most molecules, absorption wavelengths corresponding to transitions between the ground state and any vibrational level of the first excited state, fall in the range of ultraviolet and visible light. Low-energy transitions are also possible between vibrational levels within a single electronic level. These transitions produce radiation in the infrared range.

The figure on the right illustrates the relationship between specific energy transitions in the energy level diagram (upper graph) and the absorbance spectrum (lower graph).

39 Fundamentals of Spectroscopy Aug ‘17 Absorption for Biological tissues

The figure below shows the primary absorption spectra of biological tissues. Also shown are the absorption coefficients at some typical laser wavelengths.

There are several major contributors to the absorption spectrum: -In the ultraviolet, the absorption increases with shorter wavelength due to protein, DNA and other molecules. - In the infrared, the absorption increases with longer wavelengths due to tissue water content. Scaling the pure water absorption by 75% mimics a typical tissue with 75% water content. - In the red to near-IR (NIR), absorption is minimal. This region is called the diagnostic and therapeutic window. - Whole blood is a strong absorber in the red-NIR regime, but because the volume fraction of blood is a few percent in tissues, the average absorption coefficient that affects light transport is moderate. However, when photons strike a blood vessel they encounter the full strong absorption of whole blood. Hence, local absorption properties govern light-tissue interactions, and average absorption properties govern light transport.

40 Fundamentals of Spectroscopy Aug ‘17 Atomic Absorption In atomic absorption, the excitation of photons promotes the electrons from a lower energy level to a higher energy level that matches exactly the differences in energies between the highest occupied orbital and some higher unoccupied orbital. (Na)

Energy-level diagram for sodium, showing the transition resulting from absorption at 590, 330 and 285nm.

41 Fundamentals of Spectroscopy Aug ‘17 UV absorption spectra

The molecular absorption consists of absorption bands that are closely spaced. Under real conditions however, the line absorption bands become broad lines. In solution, the molecules are surrounded by solvent and the bands loses more resolution and becomes a blur hump.

Typical UV spectra. The compound, 1,2,4,5-tetrazine. The figure shows an absorption spectra in the gas phase(a), in a nonpolar solvent (b), and a polar solvent (c). The spectra in (b), shows that the electronic transition but resolution of the vibrational and rotational transition is lost. The spectra in (c) shows the blending of the electronic peaks because of strong intermolecular forces.

42 Fundamentals of Spectroscopy Aug ‘17 Infrared Absorption Infrared radiation are not sufficient to cause electronic transitions, but can cause different vibrational modes in a molecule.

IR covers the range of the electromagnetic spectrum between 0.78 and 1000 mm. The wavelength is measured in "wavenumbers", which have the units cm-1. wavenumber = 1 / l (l in centimeters) It is useful to divide the infra red region into three sections; near-, mid-, and far infra red;

Region Wavelength range (µm) Wavenumber range (cm-1) Near 0.78 - 2.5 12800 - 4000 Middle 2.5 - 50 4000 - 200 Far 50 -1000 200 - 10 The most useful I.R. region lies between 4000 - 670cm-1

TypeType of of molecular molecular vibrations. vibrations. The The arrows arrows shows shows thethe direction direction of of the the movement movement and and the the plus plus and and minusminus indicate indicate the the motion motion in in or or out out of of the the plane. plane.

43 Fundamentals of Spectroscopy Aug ‘17 Fluorescence and Phosphorescence

The emission process after absorption of radiation can take one of two photoluminescence pathways towards relaxation. Fluorescence is a rapid transition (10-5 or less) while Phosphorescence may take minutes or hours after the irradiation. A third non- photoluminescence pathway is the non-radiative relaxation.

Energy-level diagram showing some of the energy changes that occur during absorption, nonradiative relaxation and fluorescence by a molecular species

44 Fundamentals of Spectroscopy Aug ‘17 … and Phosphorescence

After an electron absorbs a photon of high energy, it may undergo vibrational relaxations and intersystem crossing to another spin state. Again the system relaxes vibrationally in the new spin state and eventually emits light by phosphorescence.

45 Fundamentals of Spectroscopy Aug ‘17 Emission of Electromagnetic Radiation

Emission of a brine sample obtained in an oxyhydrogen flame. Lines of sodium, potassium, strontium, calcium and magnesium are identified. The transition for the spectrum is shown. Chemical species can emit light by (1) bombardment with electrons; (2) heating in a plasma, a flame or electric arc; (3) irradiation with a beam of light.

Real

46 Fundamentals of Spectroscopy Aug ‘17 Summary of modes of Spectroscopy

A schematic level scheme of an organic molecule which includes the three main electronic states involved in absorption, fluorescence, and intersystem crossing is shown below. (The scheme is a Jablonski diagram).

47 Fundamentals of Spectroscopy Aug ‘17