Spectroscopy (Topics 8,10,12,14,15) Flashcards
What does the de Broglie relation allow us to conclude?
Particles with low linear momentum have long wavelengths and vice versa
Which type of transitions in a molecule is likely to be induced by photons with a wavelength in the microwave region?
Vibrational
What is spectoscopy?
the study of the interaction of electromagnetic
radiation with matter
How and why things scatter, absorb, or emit light
Exchange of energy between radiation and matter
Electromagnetic radiation is
Light
Oscillating electric and magnetic fields that propagate as a wave
c =
speed of light : 2.998 x 10^8 ms^-1
π (wavelength (m)) x π (frequency (Hz = s^-1)
π =
The wavelength at which a substance has itβs strongest photon absorption
β (6.626 x 10^-34 Js) / π (mass(kg)) x π£ (velocity (ms^-1))
angular frequency π
2 π π (frequency (s^-1)
2 π / T (s)
π (1D)
ππ/2πΏ
1 / 2π (ππ / ππππ)^1/2
π~ (wavenumber (cm^-1) =
π (s^-1) / c (2.998 x 10^8 ms^-1)
1 / 2πc (ππ / ππππ)^1/2
π (1D) =
2πΏπ/π
ππ₯^2 + ππ¦^2 + ππ§^2 (3D)
4πΏ^2π^2 / C^2
Infrared radiation frequency
n ~10^12 β 10^13 s-1
Visible light radiation frequency
n ~10^14 s-1
Planck Constant β =
β =
6.626 x 10^-34 Js
β / 2 pi
Planck-Einstein Relation:
πΈ (J) = β (6.626 x 10^-34 Js) x π (frequency (s^-1))
πΈ = ππ^2
πΈ^2 =
So for a photon, πΈ =
πΈ^2 = (ππ^2)^2 + (ππ)^2
πΈ = ππ
πΈ (energy (J))
π (mass (kg))
π (momentum (kg m s^-1)
π (speed of light (2.998 x 10^8 ms^-1))
Einstein mass-energy relation
E = mc^2
de Broglie Wavelength
lambda (wavelength (m)) = β (6.626 x 10^-34 Js or kg m^2 s^-1 / π (mass(kg)) π£ (velocity(m s^-1))
How do you define a peak?
Peak position
Peak intensity
Peak breadth
delta E =
E1 - E0
Bohr condition
Photon energy βπ must be equal to delta E in order for a transition to occur
π (excited state lifetime)=
1 / A1->0
Peak intensity information
Population
Transition Probability
State Degeneracy
Experimental: Path length of sample
Boltzmann expression
π(π½) / π= π(π½) π^β (πΈ(π½) ππ)
πΈ(π½) = π΅~βππ½(π½ + 1)
π(π½) = 2π½ + 1
(J) subscript
N upper / N lower =
πβ^(βπΈ ππ)
At room temp (298K), kT =
200 cm^-1
Most critical factor in determining selection rules and line intensities
Transition dipole moment
Measure of the electric dipole moment associated with movement of
charge from its initial state (state 0) to its final state (state n)
Gross Selection rule
In order for a transition to occur,
it must have a nonzero transition dipole moment
In order for an atom or molecule to
absorb/emit a photon at a specific frequency, it must possess
(at least transiently) a dipole oscillating at that frequency
π΄ = ππΏπ units
Absorbance (unit less) = molar extinction coefficient (M^-1 cm^-1) x sample thickness (often 1cm) x concentraTion (M)
Commonly used versions of Beer-Lambert Law
π΄ = ππΏπ
log (πΌ0/πΌ) = ππΏπ
log (πΌ0/πΌ) = ππΏ[π] = πΌπΏ
πΌ = transmitted light intensity
π = molar extinction coefficient (M^-1 cm^-1)
πΏ = sample thickness (often 1cm)
π = concentration (M)
π = absorption cross section
[π] = Concentration (molecule cm^-3)
πΌ = absorption coefficient
Heisenberg Uncertainty
ΞπΈΞπ‘ >/=
β / 2π
Microwave wavelength
1cm - 100 um
Infra-red wavelength
1um - 100 um
Visible light wavelength
400 - 700 nm
Order of energies for 3 spectroscopies
Delta E elec»_space; Delta E vib»_space; Delta E rot
Rotational energies are in β¦ region of electromagnetic
spectrum
(microwave)
1 β 100 cm^-1
πΌ (moment of inertia) =
Sum of (π) ππππ^2
π is subscript
ππ^2
πΉπ½ =
π½ is subscript
πΉ~(π½) =
(rotational energy levels)
π΅π½(π½ + 1)
π΅~π½ (π½ + 1) or π΅~π½ (π½ + 1) - π·~(π½)π½^2(π½ + 1)^2
(π½) is subscript
π΅ (cm^-1)=
π΅~ (rotational constant (cm^-1) =
β^2 / 2πΌ
β / 4πππΌ
β / 8π^2cπΌ
π~ (wavenumber (cm^-1) (π½ + 1 β π½) =
2π΅~(π½ + 1)
2π΅~(π½ + 1) - 4π·~(π½) (π½ + 1)^3
First J subscript
What will will result in a βred shiftβ
Increase in the wavelength of a wave with respect to the detector
Decrease in the wavenumber of a wave with respect to the detector
Decrease in the frequency of a wave with respect to the detector
For the Doppler broadening of a peak, what affects the width of the observed peak?
The temperature and the peak position
What function can be used to describe a peak in a spectrum?
Gaussian function
What will cause deviationes in the linearity of the Beer-Lambert law?
Changes in the refractive index at high analyte concentration
Fluorescence or phosphorescence of the sample
Scaterring of light due to particulates in the sample
The lifetime broadening of a spectral line arises from
The Heisenberg uncertainty principle
What are considered absorption and emission processes in spectroscopy
Spontaneous emission and stimulated absorption
The intensity of the spectroscopy transition can be predicted from
The population of the initial state and degeneracy
In the Beer-Lambert law, the graphical representation of
-log(10) of transmittance versus concentration of a solution can be fitted using
a linear regression
π (Potential energy (J))
π = 1/2 ππ π₯^2
ππ = spring force constant (Nm^-1)
π is subscript
π₯ = π β ππ
ππ = distance away from equilibrium (m)
π is subscript
πΊ~(v) =
(vibrational energy levels)
(v + 1/2) π~
(v + 1/2) π~ - (v + 1/2)^2 π₯π π~ (anharmonic)
π₯π = Unitless anharmonicity constant, π subscript
πΈv =
(vibrational energy)
(v + 1 / 2) βπ
π =
(ππ / ππππ)^1/2
Gross Selection Rule
Dipole must change with
displacement
From selection rules, transitions are only allowed forβ¦
(P, Q, R)
π«π― = Β±π
π«J = Β±π
P: π« J = β1
Q: π« J = 0
R: π« J = +1
π~ (v, π½ ) =
(transition energy levels)
πΊ~(v) + πΉ~(π½) = (v + 1/2) π~ + π΅~π½(π½ + 1)
Ξπ~π (v, π½)
π is subscript
π~π(π½) = π~ - 2π΅~π½
π is subscript
π~ β (π΅~1 + π΅~0)π½ + (π΅~1 - π΅~0)π½^2
Ξπ~π (v, π½)
π is subscript
π~π(π½) = π~
π is subscript
π~ + (π΅~1 - π΅~0)π½(π½ + 1)
Ξπ~π
(v, π½)
π
is subscript
π~π
(π½) = π~ + 2π΅~(π½ + 1)
π
is subscript
π~ + (π΅~1 + π΅~0)(π½ + 1) + (π΅~1 - π΅~0)(π½ + 1)^2
Rotational spectroscopy rotors
rigid rotor and non-rigid rotor
Vibrational spectroscopy oscillators
harmonic oscillators and anharmonic oscillators
π΅v =
π΅e β πΌe(v + 1/2)
e subscript
π΅e: Rotational constant at the
equilibrium structure
πΌ: Constant, reflects shape of
potential energy curve
Combination difference to the same J level
π~π (π½-1) - π~π(π½+1) = 4 π΅~0 (π½ + 1/2)
Combination difference from the same J level
π~π (π½) - π~π(π½) = 4 π΅~1 (π½ + 1/2)
Number of vibrational normal nodes
3N β 5 for a linear molecule
and 3N β 6 for a nonlinear molecule
ΞG~
v = 0 β 1 (fundamental):
πΊ~(v + 1) - πΊ~(v) =
(v + 3/2) π~ - (v + 3/2)^2 π₯π π~ - (v + 1/2) π~ + (v + 1/2)^2 π₯π π~ (using G~ equation) =
π~ - 2(v + 1) π₯π π~
ΞG~
v = 0 β 2 (1st overtone)
πΊ~(v + 2) - πΊ~(v) =
(v + 5/2) π~ - (v + 5/2)^2 π₯π π~ - (v + 1/2) π~ + (v + 1/2)^2 π₯π π~ (using G~ equation) =
2π~ - 2(2v + 3) π₯π π~
Which one of the following functions best describes the simple harmonic oscillator?
y = Ax^2
At which frequency is the R(0) transition located?
π + 2B
In the simple harmonic oscillator model for a diatomic molecule, steeper slopes of the parabola indicates
stronger bond between the atoms in the molecule
The first P-branch transition is
P(0)
Parameters that can affect the full-width-at-half-maximum of an observed optical transition in a spectrum?
Temperature
The lifetime in an excited state
The phase of the medium
Atomic mass of the species
Parameters that can affect the
intensity (height) of an observed peak in a microwave spectrum?
The instrument resolution
The degeneracy of the rotational energy levels involved in the transition
The temperature
The rotational transition dipole moment
π΅~π
Rotational constant for the equilibrium bond length of the molecule. It corresponds to the rotational constant when the molecule is in its lowest vibrational state, assuming no vibrational excitation. It provides the most fundamental measure of the moleculeβs moment of inertia in its equilibrium configuration
π΅~0
the rotational constant for the molecule when it is in its vibrational ground state (v=0). It accounts for the slight increase in bond length due to zero-point vibrational motion even in the ground state. The value of π΅~0 is typically slightly less than π΅~π because the average bond length is longer due to the vibrations
π΅~1
This is the rotational constant for the first vibrational excited state (v=1). The bond length further increases when the molecule is vibrationally excited, leading to an even larger moment of inertia and thus a smaller rotational constant compared to π΅~0
Fundamental band
the transition from the ground vibrational state (v=0) to the first excited vibrational state (v=1) in a molecule. This is the most basic and usually the most intense absorption band observed in vibrational spectroscopy.
Hot bands
transitions that originate from vibrationally excited states higher than the ground state. These transitions occur when a molecule that is already in an excited vibrational state (v=1, v=2, etc.) absorbs additional energy and transitions to an even higher vibrational state (v=2βv=3, v=3βv=4, etc.)
energy difference of hΞ½
