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Year 1 Physical Chemistry > Spectroscopy (Topics 8,10,12,14,15) > Flashcards

Spectroscopy (Topics 8,10,12,14,15) Flashcards

1
Q

What does the de Broglie relation allow us to conclude?

A

Particles with low linear momentum have long wavelengths and vice versa

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2
Q

Which type of transitions in a molecule is likely to be induced by photons with a wavelength in the microwave region?

A

Vibrational

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3
Q

What is spectoscopy?

A

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

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4
Q

Electromagnetic radiation is

A

Light
Oscillating electric and magnetic fields that propagate as a wave

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5
Q

c =

A

speed of light : 2.998 x 10^8 ms^-1
πœ† (wavelength (m)) x 𝜈 (frequency (Hz = s^-1)

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6
Q

πœ† =

A

The wavelength at which a substance has it’s strongest photon absorption
β„Ž (6.626 x 10^-34 Js) / π‘š (mass(kg)) x 𝑣 (velocity (ms^-1))

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7
Q

angular frequency πœ”

A

2 πœ‹ 𝜈 (frequency (s^-1)
2 πœ‹ / T (s)

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8
Q

𝜈 (1D)

A

𝑛𝑐/2𝐿
1 / 2πœ‹ (π‘˜π‘“ / π‘šπ‘’π‘“π‘“)^1/2

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9
Q

𝜈~ (wavenumber (cm^-1) =

A

𝜈 (s^-1) / c (2.998 x 10^8 ms^-1)
1 / 2πœ‹c (π‘˜π‘“ / π‘šπ‘’π‘“π‘“)^1/2

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10
Q

𝑛 (1D) =

A

2𝐿𝜈/𝑐

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11
Q

𝑛π‘₯^2 + 𝑛𝑦^2 + 𝑛𝑧^2 (3D)

A

4𝐿^2𝜈^2 / C^2

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12
Q

Infrared radiation frequency

A

n ~10^12 – 10^13 s-1

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13
Q

Visible light radiation frequency

A

n ~10^14 s-1

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14
Q

Planck Constant β„Ž =
ℏ =

A

6.626 x 10^-34 Js
ℏ / 2 pi

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15
Q

Planck-Einstein Relation:

A

𝐸 (J) = β„Ž (6.626 x 10^-34 Js) x 𝜈 (frequency (s^-1))

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16
Q

𝐸 = π‘šπ‘^2
𝐸^2 =
So for a photon, 𝐸 =

A

𝐸^2 = (π‘šπ‘^2)^2 + (𝑝𝑐)^2
𝐸 = 𝑝𝑐
𝐸 (energy (J))
π‘š (mass (kg))
𝑝 (momentum (kg m s^-1)
𝑐 (speed of light (2.998 x 10^8 ms^-1))

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17
Q

Einstein mass-energy relation

A

E = mc^2

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18
Q

de Broglie Wavelength

A

lambda (wavelength (m)) = β„Ž (6.626 x 10^-34 Js or kg m^2 s^-1 / π‘š (mass(kg)) 𝑣 (velocity(m s^-1))

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19
Q

How do you define a peak?

A

Peak position
Peak intensity
Peak breadth

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20
Q

delta E =

A

E1 - E0

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21
Q

Bohr condition

A

Photon energy β„Žπœˆ must be equal to delta E in order for a transition to occur

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22
Q

𝝉 (excited state lifetime)=

A

1 / A1->0

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23
Q

Peak intensity information

A

Population
Transition Probability
State Degeneracy
Experimental: Path length of sample

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24
Q

Boltzmann expression

A

𝑁(𝐽) / 𝑁= 𝑔(𝐽) 𝑒^βˆ’ (𝐸(𝐽) π‘˜π‘‡)
𝐸(𝐽) = 𝐡~β„Žπ‘π½(𝐽 + 1)
𝑔(𝐽) = 2𝐽 + 1
(J) subscript

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25
Q

N upper / N lower =

A

π‘’βˆ’^(βˆ†πΈ π‘˜π‘‡)

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26
Q

At room temp (298K), kT =

A

200 cm^-1

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27
Q

Most critical factor in determining selection rules and line intensities

A

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)

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28
Q

Gross Selection rule

A

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

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29
Q

𝐴 = πœ€πΏπ‘ units

A

Absorbance (unit less) = molar extinction coefficient (M^-1 cm^-1) x sample thickness (often 1cm) x concentraTion (M)

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30
Q

Commonly used versions of Beer-Lambert Law
𝐴 = πœ€πΏπ‘

A

log (𝐼0/𝐼) = πœ€πΏπ‘
log (𝐼0/𝐼) = 𝜎𝐿[𝑁] = 𝛼𝐿
𝐼 = transmitted light intensity
πœ€ = molar extinction coefficient (M^-1 cm^-1)
𝐿 = sample thickness (often 1cm)
𝑐 = concentration (M)
𝜎 = absorption cross section
[𝑁] = Concentration (molecule cm^-3)
𝛼 = absorption coefficient

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31
Q

Heisenberg Uncertainty
Δ𝐸Δ𝑑 >/=

A

β„Ž / 2πœ‹

32
Q

Microwave wavelength

A

1cm - 100 um

33
Q

Infra-red wavelength

A

1um - 100 um

34
Q

Visible light wavelength

A

400 - 700 nm

35
Q

Order of energies for 3 spectroscopies

A

Delta E elec&raquo_space; Delta E vib&raquo_space; Delta E rot

36
Q

Rotational energies are in … region of electromagnetic
spectrum
(microwave)

A

1 – 100 cm^-1

37
Q

𝐼 (moment of inertia) =

A

Sum of (𝑖) π‘šπ‘–π‘Ÿπ‘–^2
𝑖 is subscript
πœ‡π‘Ÿ^2

38
Q

𝐹𝐽 =
𝐽 is subscript
𝐹~(𝐽) =
(rotational energy levels)

A

𝐡𝐽(𝐽 + 1)
𝐡~𝐽 (𝐽 + 1) or 𝐡~𝐽 (𝐽 + 1) - 𝐷~(𝐽)𝐽^2(𝐽 + 1)^2
(𝐽) is subscript

39
Q

𝐡 (cm^-1)=
𝐡~ (rotational constant (cm^-1) =

A

ℏ^2 / 2𝐼
ℏ / 4πœ‹π‘πΌ
β„Ž / 8πœ‹^2c𝐼

40
Q

𝜈~ (wavenumber (cm^-1) (𝐽 + 1 ← 𝐽) =

A

2𝐡~(𝐽 + 1)
2𝐡~(𝐽 + 1) - 4𝐷~(𝐽) (𝐽 + 1)^3
First J subscript

41
Q

What will will result in a β€œred shift”

A

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

42
Q

For the Doppler broadening of a peak, what affects the width of the observed peak?

A

The temperature and the peak position

43
Q

What function can be used to describe a peak in a spectrum?

A

Gaussian function

44
Q

What will cause deviationes in the linearity of the Beer-Lambert law?

A

Changes in the refractive index at high analyte concentration
Fluorescence or phosphorescence of the sample
Scaterring of light due to particulates in the sample

45
Q

The lifetime broadening of a spectral line arises from

A

The Heisenberg uncertainty principle

46
Q

What are considered absorption and emission processes in spectroscopy

A

Spontaneous emission and stimulated absorption

47
Q

The intensity of the spectroscopy transition can be predicted from

A

The population of the initial state and degeneracy

48
Q

In the Beer-Lambert law, the graphical representation of
-log(10) of transmittance versus concentration of a solution can be fitted using

A

a linear regression

49
Q

𝑉 (Potential energy (J))

A

𝑉 = 1/2 π‘˜π‘“ π‘₯^2
π‘˜π‘“ = spring force constant (Nm^-1)
𝑓 is subscript
π‘₯ = π‘Ÿ βˆ’ π‘Ÿπ‘’
π‘Ÿπ‘’ = distance away from equilibrium (m)
𝑒 is subscript

50
Q

𝐺~(v) =
(vibrational energy levels)

A

(v + 1/2) 𝜈~
(v + 1/2) 𝜈~ - (v + 1/2)^2 π‘₯𝑒 𝜈~ (anharmonic)
π‘₯𝑒 = Unitless anharmonicity constant, 𝑒 subscript

51
Q

𝐸v =
(vibrational energy)

A

(v + 1 / 2) β„πœ”

52
Q

πœ” =

A

(π‘˜π‘“ / π‘šπ‘’π‘“π‘“)^1/2

53
Q

Gross Selection Rule

A

Dipole must change with
displacement

54
Q

From selection rules, transitions are only allowed for…
(P, Q, R)

A

𝚫𝐯 = ±𝟏
𝚫J = ±𝟏
P: 𝚫 J = –1
Q: 𝚫 J = 0
R: 𝚫 J = +1

55
Q

𝑆~ (v, 𝐽 ) =
(transition energy levels)

A

𝐺~(v) + 𝐹~(𝐽) = (v + 1/2) 𝜈~ + 𝐡~𝐽(𝐽 + 1)

56
Q

Δ𝑆~𝑃 (v, 𝐽)
𝑃 is subscript

A

𝜈~𝑃(𝐽) = 𝜈~ - 2𝐡~𝐽
𝑃 is subscript
𝜈~ βˆ’ (𝐡~1 + 𝐡~0)𝐽 + (𝐡~1 - 𝐡~0)𝐽^2

57
Q

Δ𝑆~𝑄 (v, 𝐽)
𝑄 is subscript

A

𝜈~𝑄(𝐽) = 𝜈~
𝑄 is subscript
𝜈~ + (𝐡~1 - 𝐡~0)𝐽(𝐽 + 1)

58
Q

Δ𝑆~𝑅 (v, 𝐽)
𝑅 is subscript

A

𝜈~𝑅 (𝐽) = 𝜈~ + 2𝐡~(𝐽 + 1)
𝑅 is subscript
𝜈~ + (𝐡~1 + 𝐡~0)(𝐽 + 1) + (𝐡~1 - 𝐡~0)(𝐽 + 1)^2

59
Q

Rotational spectroscopy rotors

A

rigid rotor and non-rigid rotor

60
Q

Vibrational spectroscopy oscillators

A

harmonic oscillators and anharmonic oscillators

61
Q

𝐡v =

A

𝐡e βˆ’ 𝛼e(v + 1/2)
e subscript
𝐡e: Rotational constant at the
equilibrium structure
𝛼: Constant, reflects shape of
potential energy curve

62
Q

Combination difference to the same J level

A

𝜈~𝑅 (𝐽-1) - 𝜈~𝑃(𝐽+1) = 4 𝐡~0 (𝐽 + 1/2)

63
Q

Combination difference from the same J level

A

𝜈~𝑅 (𝐽) - 𝜈~𝑃(𝐽) = 4 𝐡~1 (𝐽 + 1/2)

64
Q

Number of vibrational normal nodes

A

3N – 5 for a linear molecule
and 3N – 6 for a nonlinear molecule

65
Q

Ξ”G~
v = 0 β†’ 1 (fundamental):

A

𝐺~(v + 1) - 𝐺~(v) =
(v + 3/2) 𝜈~ - (v + 3/2)^2 π‘₯𝑒 𝜈~ - (v + 1/2) 𝜈~ + (v + 1/2)^2 π‘₯𝑒 𝜈~ (using G~ equation) =
𝜈~ - 2(v + 1) π‘₯𝑒 𝜈~

66
Q

Ξ”G~
v = 0 β†’ 2 (1st overtone)

A

𝐺~(v + 2) - 𝐺~(v) =
(v + 5/2) 𝜈~ - (v + 5/2)^2 π‘₯𝑒 𝜈~ - (v + 1/2) 𝜈~ + (v + 1/2)^2 π‘₯𝑒 𝜈~ (using G~ equation) =
2𝜈~ - 2(2v + 3) π‘₯𝑒 𝜈~

67
Q

Which one of the following functions best describes the simple harmonic oscillator?

A

y = Ax^2

68
Q

At which frequency is the R(0) transition located?

A

𝜈 + 2B

69
Q

In the simple harmonic oscillator model for a diatomic molecule, steeper slopes of the parabola indicates

A

stronger bond between the atoms in the molecule

70
Q

The first P-branch transition is

A

P(0)

71
Q

Parameters that can affect the full-width-at-half-maximum of an observed optical transition in a spectrum?

A

Temperature
The lifetime in an excited state
The phase of the medium
Atomic mass of the species

72
Q

Parameters that can affect the
intensity (height) of an observed peak in a microwave spectrum?

A

The instrument resolution
The degeneracy of the rotational energy levels involved in the transition
The temperature
The rotational transition dipole moment

73
Q

𝐡~𝑒

A

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 molecule’s moment of inertia in its equilibrium configuration

74
Q

𝐡~0

A

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 𝐡~0 is typically slightly less than 𝐡~𝑒 because the average bond length is longer due to the vibrations

75
Q

𝐡~1

A

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 𝐡~0

76
Q

Fundamental band

A

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.

77
Q

Hot bands

A

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=2β†’v=3, v=3β†’v=4, etc.)
energy difference of hΞ½

Year 1 Physical Chemistry (3 decks)

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