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Chapters 17, 19

Relation between frequency and wavelength

νλ=c (vacuum)
νλ=c/n (anywhere other than a vacuum, where n is the refractive index)

Relation between energy and frequency

E = hv

Energy ~ (wavelength, wavenumber)

Energy is inversely proportional to wavelength (λ) and directly proportional to wavenumber (1/λ)



Electromagnetic spectrum (low energy --> high energy)

radiowave, microwave, infrared (IR), visible, UV, x-ray, gamma-ray

Visible wavelength range and color order

400nm --> 800 nm
violet - blue - green - yellow - orange - red

Irrandiance (P)

energy per second per unit area of the light beam

Simple set up of single-beam spectrophotometry experiment

Light source --> wavelength selector (monochromator) --> [P0] Sample [P] --> Light Detector

Note: where Sample has the length "b"

Transmittance (T)

P(after sample)/P(before sample)

Absorbance (A)

-log(T) = εbc

Note: Absorbance is directly proportional to (molar absorptivity, cell length and sample concentration)
Transmittance (T) is NOT proportional to concentration, always do the conversion to A before multiplying out


Part of the molecule that is responsible for light absorption

What does your eye see?

Your eye sees the colors that are NOT absorbed.
For instance, sample absorbed yellow, you see only blue light
Science says: "the observed color is called the complement of the absorbed color"

What does the color we perceive depend on?

1) wavelength
2) light intensity

When does Beer's law fail?

1) when radiation is not monochromatic
2) when solutions are not dilute

So: use monochromatic light and make sure that your solution is dilute enough to that the molar absorptivity does not change

Sample Cell

Visible: glass cuvet
UV: fused-silica cuvet (no glass for UV since glass absorbs UV light)
IR: cells constructed with NaCL or KBr (basically, SALTS)
Far-IR: polyethylene (which is a fancy word for plastic) is a transparent window

the relation between path length and dilution?

The more dilute, the longer the pathlength needs to be, so:
Pathlength: solid < liquid < gas
--> Gases need the longest pathlengths

How to assemble spectrophotometers by light type (Vis, UV, IR)

--> Tungsten
--> prism (can be glass) monochromator, grating (anything shiny will work)
--> glass cuvet
--> photo diodes (for photoelectric effect), photomultiplier

--> Deuterium
--> pure silicon dioxide prism, grating (ONLY aluminum)
--> fused silica cuvet
--> photo diodes (for photoelectric effect), photomultiplier (don't use real light for this!)

IR: (this is detected by heat! gives off lots of it)
--> Globar
--> grating (only copper and gold, things with "red tones")
--> salt/plastic cuvet
--> Thermocouples (two metals) or Solid-state detectors (semi-conductors) e.g. GOLAY CELL, deuterated triglycerine sulfate, mercury cadmium telluride

For IR: the heavier the salt, the better
IR is also the only one that can operate in air, the others need to be vacuum

Why do we choose the wavelength of max absorbance for spectrophotometric analysis?

MAXIMUM Absorbance wavelength:
1) sensitivity is greatest at maximum absorbance
2) curve is relatively flat at maximum, so there is little variation (easier on monochromator drift)

What waves cause what action in molecules?

gamma-rays: nucleus (nuclear energy level transition)
x-rays: inner-electrons (core electron transition)
UV: outer-electrons (valence electron transition)
IR: molecular vibration transition
Microwaves: molecular rotation transition
Radiowaves: miss everything

Spectrophotometric titration

monitor absorbance during titration to see when equivalence point is reached ("as the sample changes color, we can tell how much of whatever is being created")

How to correct absorbance for the effect of dilution? (formula)

A(corrected) = A(observed)*(total volume/initial volume)

A(corrected) is always greater than A(observed)

Characteristic of Singlet State

spins are opposed (n, π*)

Characteristic of Triplet State

spins are concordant (n, π*)

Physical Processes that happen when molecules absorb energy

Internal conversion
Intersystem crossing

What type of emission can come from S₁?


What type of emission can come from T₁


Which emission energy type is higher and what is the resulting wavelength situation?

Energy: Phosphorescence < Fluorescence (the T's just have a **** time of things in general)
and so,
Wavelengths: Phosphorescence > Fluorescence (weaker, wider waves)

Luminescence, definition

emission of light from an excited state of a molecule (phosphorescence (S) and fluorescence (T) are types of luminescence

Note: luminescence is inherently more sensitive than absorption (stadium lights example), where luminescence is the good version of the story, absorption the bad

Relation between Absorption and Emission Spectra

fluorescence and phosphorescence come out at lower energy than absoprtion (excitation energy)

So: molecules emit longer wavelengths than they absorb

Definition of Fluorescence vs. phosphorescence

Fl: emission of light with no change to electronic spin state
Phos: emission of light WITH change to electronic spin state

What is Rayleigh scattering vs. Raman scattering?

Rayleigh scattering: molecules oscillate in the frequency of incoming radiation and emit that same frequency in all directions
Raman scattering: molecules extract a quantum of vibrational energy from incoming light and scatter light with less energy

What is the definition of Molarity (formula form)?

M (Molarity) = Moles/Liter

Units: M = mol/Lb

What is the definition of moles (formula form)?

mol (moles) = grams / molecular weight

Units: mol = g/MW

what is the definition of molecular weight (formula form)

MW (molecular weight) = grams/moles

Units: MW = g/mol

Lessons from Photometric Error

Absolute error: Δx

Relative error: Δx/x (the error as a fraction of the measurement)

--> Usually relative error is more important

Transmittance to relative uncertainty in concentration

U-shaped curve, be sure to get mid-range transmittance

Solutions to extreme Transmittance levels

T~ 0 (very little light is transmitted)
1) dilute sample (concentration is too high!)
2) use a shorter path cell (that's making b smaller, thus A smaller, thus T larger)

T~1 (lots of light is transmitted)
1) use a longer path cell
2) changing concentration is not really an option here,since it's difficult to make things MORE concentrated

Stray Light questions, what do you use and what's the main formula?

Have to use transmittance!

T = P/P₀

When you want the apparent light you add to the P's
When you want the true light you subtract the P's

Apparent light will ALWAYS be greater than the true light (transmittance)

Signal 2 Noise Ratio Questions

take the square root of the factor between the two spectra #s

Large to small: division
Small to large: multiplication

1000 --> 1 means you divide by the square root of 1000
20 --> 400 means that you multiply by the square root of 20

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