spectroscopy theory and instrumentation

C, lambda, and nu relation

C = λv

wavenumber units

inverse cm

what is v̄

wavenumbers, or 1/λ

Energy relations

E = hv = hc/λ = hcv̄

Lowest to highest energy EM spectrum

Radio waves, Microwave, Infrared, Visible, UV, X ray, Gamma rays

visible light spectrum

800nm (red, low energy) to 400nm (blue, high energy)

reflection

light bounces off hard surface

what are often used in optics of instruments

mirrors, prisms

attenuated total reflection can…

…be used as a spectroscopy technique (IR)

refraction

bending of light after passing between two different media

ex: prism monochromators

diffraction

bending of light after passing through a small opening

ex: x-ray diffraction and grating monochromators

describe absorption of light

transition from ground electronic state to higher energy level through added light energy

describe emission of light

transition from higher energy level to lower (or ground) electronic state through release of light energy

true or false: all transitions are allowed

false

What is the first selection rule (equation and words)

Ephoton = hv= ∆Etransition

the energy of the photon must be equal to the energy needed for the transition

what is the second selection rule

Spin Selection Rule: Electron spin cannot change during a transition.

• The total spin change must be zero ($\Delta S = 0$)

• Spin multiplicity ($2S + 1$) must remain the same in the ground and excited states (e.g., singlet to singlet)

what is the third selection rule

change in dipole needed for IR

sigma to sigma star, pi to pi star for UV vis

atoms have only __ states

electronic

spacing between energy levels is ___ in atoms

large

solution spectra are..

…broadened due to collisions and solvent

excited states will __ __ ___ to the __ __

relax back down, ground state

radiative emission

atom emits photon with energy matching energy gap

non radiative emission

atom relaxes without emission of photon

• collisional deactivation

• release energy as heat to solvent

molecules can emit a photon ____ or with ___

spontaneously, stimulation

sources of atomic emission

• line sources

• excitation through electrical means

What is the primary difference in timing and mechanism between fluorescence and phosphorescence?

• Fluorescence happens rapidly as a molecule drops from a singlet state (to the ground state

• Phosphorescence is much slower (seconds to hours) because it involves a "forbidden" spin flip, dropping from a triplet state to the ground state

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How do electron spins differ between a singlet state and a triplet state in a Jablonski diagram?

• In a singlet state all electron spins are paired (opposite directions).

• In a triplet state the excited electron undergoes a spin flip and becomes parallel (same direction) to its partner.

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Identify which processes on a Jablonski diagram emit a photon (radiative) and which release heat (non-radiative).

• Radiative (Emits light): Fluorescence and Phosphorescence.

• Non-Radiative (Emits heat): Vibrational Relaxation, Internal Conversion (IC), Intersystem Crossing (ISC), and External Conversion (EC).

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What dictates whether a non-radiative transition is classified as Internal Conversion (IC) or Intersystem Crossing (ISC)?

Internal Conversion (IC): Occurs between states of the same spin multiplicity

Intersystem Crossing (ISC): Occurs between states of different spin multiplicities

What are the five basic components of a spectrometer

radiation source, wavelength selection, sample containement, radiation detector, signal processing and reading

What do you want in a radiation source

high intensity output

flat intensity vs wavelength response

low source intensity variability

two main types of radiation sources

line and continuous

Characteristics of continuous radiation sources

• emits over large range of wavelengths

• many based on blackbody radiation

• intensity and wavelength are a function of T

• max wavelength is inversely proportional to T

examples of continuous radiation sources

Infrared - globar and nichrome wire

visible - tungsten lamp

ultraviolet - deuterium or xenon lamp, high pressure mercury arc lamp

examples of line sources

low pressure metal vapor lamps - Na and Hg

hollow cathode lamp - element specific

Lasers basics

• stimulated emission of radiation

• need 3-4 quantum states w appropriate lifetimes

• give high intensity monochromatic coherent light

What is the problem with lasers

rate of emission/absoprtion is proportional to number of molecules in excited/ground state

• need more population in excited state

• no two level systems

what is a monochromator’s function

seperate light frequencies with dispersion to select a single wavelength from a broadband light source

what are the three types of monochromators

filter, prism, grating

Filters basics

• polychromator

• low pass: absorb wavelengths above cutoff

• high pass: absorb wavelengths below cutoff

• notch: high and low wavelength cutoffs

Prism basics

• refraction of light → seperate light by dispersion

• combined with an exit slit

Prism materials

UV - quartz

visible - glass

IR - NaCl or KBr

True or false: prisms disperse all wavelengths equally in space

false

seperation in dispersion is better at…

…short wavelengths

fixed slits cause different…

…bandwiths

grating basics

• diffraction off of finely spaced grating

• different wavelengths in phase at different points along plane

• rotating grating → change wavelength

• normal dispersion, not wavelength dependent

problem with grating..

Multiple lower-wavelength harmonics will diffract at the exact same angle as the fundamental wavelength, meaning they all get through together.

solution to overlapping harmonics in grating

• Place optical filters in the path to block the shorter, lower-wavelength harmonics.

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What is the Bragg’s Law formula

𝑛𝜆=2𝑑sin(𝜃)

what do n =1 and n = 2 to infinity represent in Bragg’s Law

n = 1 → fundamental wavlength

n = 2 to infinity → higher order harmonics

How do you find the line spacing (𝑑) and the 2nd harmonic wavelength (𝜆_2) for an 800 lines/mm grating at 𝜃=33

1. find d (1/line spacing)

2. find fundamental (1*line spacing * sin(33))

3. find second harmonic (fundamental/2)

advantages of gratings over prisms

• linear dispersion

• larger usefull range

• smaller

disadvantages of gratings over prisms

• cost

• more stray light

• higher order harmonics

photovoltaic detector

range: 250-750nm

photon makes electrol-hole pair in semiconductor → creates current

intesity proportional to the number of photons

photovoltaic detector advantages

• no external power supply

• rugged

photovoltaic detector disadvantages

• limited wavelength range

• not very sensitive

phototube detector

• similar to photovoltaic but powered

• photon → ejection of electrons

• electrons collected at anode

phototube detector advantages

• more sensitive

• can work in UV and Visible range

phototube detector disadvantages

• dark current → spon. emission of electrons

• expensive

photomultiplier tube detector

• much more sensitive version of phototube

• has anodes with amplification at each step

• high gain of electrons

photomultiplier tube detector advantages

• sensitivtiy

• versatility

photomultiplier tube detector disadvantages

• dark current

• cost

photodiode array detector

• current flow only upon light excitation

• very small

• put sample between source and grating

  • single PMT → sample after grating

• replace exit slit w/ array of photodiodes

• measures all wavelengths at once

• $$ and less sensitive

IR Heat detector

• need to measure IR photons

• need to measure very small change in temperature

two types of IR heat detectors

thermocouple

golay cell

Thermocouple IR heat detector

• two unlike metals

• voltage develops at junction

• temperature and pressure dependent voltage

Golay cell IR heat detector

• temperature change (absorption) cuases change in pressure

• pressure change can be read using optical system

Lambert-Beer’s law

• light power decreased through absorption

• I = (I_0) e ^(-σ_λnl)

Calibration curve for Beer’s Law

• use internal standards

• only valid if beer’s law is linear in that concentration region

• can be used to interpolate

Describe standard addition

adding increasing amounts of standards to samples at fixed volumes

make a plot of A vs total concentration of standard added

x intercept = negative of initial concentration

C_0 formula

(A0C1)/(A1-A0)

standard addition more in depth

1. take several identical portions of unknown sample

2. leave flask 0 alone (only unknown concentration)

3. spike flasks 1,2,3 with increasing, known concentrations of a pure standard

Sample 0 (Unspiked):

𝐴0=𝑘⋅𝐶0

Sample 1:

𝐴1=𝑘(𝐶0+𝐶1)

Sample 2:

𝐴2=𝑘(𝐶0+𝐶1+𝐶2)

Most deviations from beer’s law are…

…negative deviations

to correct deviations in beer’s law, you CAN ___, but it is better to ___

interpolate, dilute

A is ___, but we usually measure ___

logarithmic, %T

error in %T is ___ and leads to ___________

constant, varying error in A

for less than 3.5% error, stay between….

… 15% and 65% or 0.82 and 0.18 (A)

Beer’s law is only accurate for what kind of solution?

Dilute solution

in beer’s law, molecules…

… should NOT be interacting with eachcother - this alters the electron cloud.

If a solution is too dilute or epsilon is too small..

.. you cannot accurately measure decrease in light intensity

what is bandwidth

range of light wavelengths getting through the monochromator.

• usually constant

• measure as close to maximum of epsilon vs lambda as possible

• small bandwidth is good

stray radiation effect

hit detector → false signal

• normally doesnt pass through signal

• A will be smaller than it should be

• can fix by cutting down on optics or painting it black

A_obs formula

-log(P+Ps/P0+Ps)

Describe why spectroscopy of atoms is simple

only sharp electronic transitions

What is the natural linewidth of atomic transitions?

Approximately 10^-5 nm.

What causes natural linewidth?

The energy–time uncertainty principle. The finite lifetime of an excited state creates uncertainty in its energy.

What causes Doppler broadening?

Random thermal motion of atoms or molecules causes Doppler shifts in transition wavelengths.

How does Doppler broadening affect a spectral peak?

It broadens the peak because particles moving at different velocities produce different frequency shifts.

What is a blue shift?

A shift to a shorter wavelength.

What is a red shift?

A shift to a longer wavelength.

What causes pressure broadening?

Interactions between particles perturb quantum energy levels, broadening spectral lines.

What four flame conditions are desirable in atomic absorption spectroscopy?

• High degree of atomization

• Low degree of excitation

• Low degree of ionization

• Minimal formation of oxides

Why should excitation be kept low in atomic absorption spectroscopy?

Atomic absorption primarily measures ground-state atoms. Excitation reduces the ground-state population.

What determines the excited-state population in a flame?

Flame temperature, according to the Boltzmann distribution.

What factors determine flame temperature?

• Fuel and oxidant

• Position within the flame

• Burner construction

Why must samples be nebulized before flame analysis?

To convert a liquid sample into a fine aerosol that can be introduced into the flame.

What is atomization in atomic absorption spectroscopy?

The process of converting the analyte into free gas-phase atoms, separating it from its chemical compounds.

What two processes are required to prepare typical liquid samples for atomic absorption analysis?

• Nebulization: Converts the liquid into an aerosol.

• Atomization: Uses heat to produce free gas-phase atoms. This involves desolvation, vaporization, and atomization.

What are the two common atomization sources in atomic absorption spectroscopy?

• Flame

• Electrothermal furnace