Electromagnetic Energy-Wave theory
•Frequency: The number of complete cycles of a periodic process occurring per unit time. Its unit is Hertz (Hz).
•Wavelength: Distance between two consecutive crest or trough is called wavelength. It can be measured in cm, μm, nm or angstrom (Å).
Where, 1 nm= 10-3μm =10-6=10-7cm =10-9m and 1 Å = 10-8cm.
•Amplitude: The maximum extent of a vibration or oscillation, measured from the position of equilibrium. It is the intensity of wave. Its unit is meter.
•Frequency shares an inverse relationship with the wavelength so that;
v = c/λ
Where; v= frequency
c= speed of light (3 x 108m/s)
•Sometimes radiation, mostly in the infrared region is characterized by another term known as the wave number and is given as;
•Wave number means the number of complete cycles occurring per centimeter.
Energy of Electromagnetic radiation- Particle theory
•Electromagnetic energy/radiation is emitted only in tiny packets or quanta of energy that were later known as photons.
•Each photon pulses with a frequency and travels with the speed of light.
•The energy of the photon of electromagnetic radiation is proportional to its frequency.
•Energy of photon= E = hv
Where, h= proportionality constant=planck’sconstant= 6.63 x 10-34J.s
& v= frequency
•Energy = Planck’s constant x frequency
or, E = h x v
or, J = Js x s-1
•Most chemical energies are quoted in Jmol-1or KJmol-1rather than in Joules for an individual atom.
•We therefore need to multiply our value of h x v by the Avogadro constant to obtain Jmol-1
•Avogadro constant = NA= 6.02 x 1023mol-1
•Energy = Avogadro constant x Planck’s constant x frequency
E = NAx h x v
Jmol-1= mol-1x J s x s-1
•Theelectromagnetic spectrumis therangeof all possible frequencies ofelectromagnetic radiation.
less than 0.01nm
more than 15EHz
more than 62.1keVX-Ray
30 EHz –30PHz
124 keV–124 eV
30 PHz –750 THz
124 eV–3 eV
770 THz –400 THz
3.2 eV–1.7 eV
400 THz –300GHz
1mm –1 meter
300 GHz–3 Hz
Laws of Absorption
Where, I = the intensity of the transmitted light,
I0= the intensity of the incident light.
b= the absorbing thickness, better known by the term path-length.
k= the linear absorption coefficient of the absorbing material. The power term in the above relationship can be removed by converting to the logarithmic form. Thus,
ln I/I0 = -kb,
or, ln I0/ I =kb------------(2)
Changing to common logarithms we get,
2.303 log10( I0/I) = kb ---------------(3)
A = abc + 0 Beer lambert law
Y = mx + c Equation of straight line
It allows us to calculate the concentration of unknown analyte.
Analysis of Mixtures of Absorbing Substances
•When the sample solution contains more than one absorbing species, the absorbance of the solution will be the sum of allabsorbances:
•At= A1+ A2+ A3+ ….
•The different constituents can be determined if we build equations equal to the number of unknowns. However, this procedure, if manually performed, is impractical due to lengthy and difficult math involved. When only two absorbing species are present, the solution is formidable and is executed by finding the absorbance of the solution at twowavelength(wavelength maximum for eachanalyte):
•ex’,ex”,ey’,ey” can be determined from standards ofanalytesx and y atl’,l” and values obtained are inserted in equations 1 and 2 where two equations in two unknowns can be easily solved.
Limitations of the Beer-Lambert law
•Samples to be studied in the UV-Vis region are usually gas or solution and are put in cells known as cuvette.
•Spectra of gases are taken using enclosed cells, with an evacuated cell as a reference. Standard path-length of gas cells is usually 1 mm but cells with path length of 0.1 to 100 mm are available for special cases.
•Most of the spectrophotometric studies are made in solution. The solutions are dispensed in cells known as cuvettes.
•Cuvette meant for ultraviolet region are made up of either ordinary glass or sometimes quartz. Since glass absorbs in the UV region, quartz or fused silica cells are used in this region. Standard path length of these cuvettes is usually 1 cm. However, cuvettes of path-length of 1 mm to 10 cm are available for special purposes.
•The surface of the cuvette must be kept very clean, free from fingerprints smudge, and traces of previous samples which might otherwise cause interference in the optical path.
Woodward-Fieser Rules for Calculating the λmax of Conjugated Dienes and Polyenes