Brainscape's Knowledge GenomeTM


Top Flashcards (Certified)
All Flashcards

Year 3 - Chemistry > Magnetic Resonance > Flashcards

Magnetic Resonance Flashcards

(95 cards)

Start Studying
1
Q

How does magnetic field strength change gap between spin states?

A

As B increases the energy gap increases

@ high B the frequency required is higher

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

What does magnetic momentum interact with?

A

Interacts with applied field to give resonance

orbit:
μs~l = γel

e- spin: μs~g0s = 2γes

nuclear spin (with spin angular momentum, uppercase i):
μN= γI

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

How does value of I change magnetic moment of a particle?

A

Non-zero spin quantum number I required to have a non-zero spin angular momentum I and therefore a magnetic moment μ

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What are the Zeeman Eigenstates?

A

A single-spin (1/2) has 2 eigenstates of angular momentum on z-axis

ψ = |I,mI>

ψ+/- 1/2 = |1/2, +/- 1/2>

where + is α and - is β

where I (uppercase i) = spin angular momemntum qn
mI = spin proj q.n

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

What are the eigenstates of the Zeeman eigenstates?

A

Izψ = mI hbar ψ

Izψ1/2 = +1/2 hbar ψ1/2

Izψ-1/2 = -1/2 hbar ψ-1/2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

What is the interaction energy between a field and a spin?

A

Classic:
E = -γ(hbar)mIB

QM:
H^onespin = -γB0I^z

H^onespinψ results in
Eα = -1/2 (hbar)γB0
Eβ = 1/2 (hbar)γB0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

What is the resonance frequency from state α -> β?

A

ν = γB0/2π

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

What are allowed transitions between spin states?

A

ΔmI = +/- 1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

What is the difference in population between α and β states?

A

Nβ/Nα = exp(-ΔE/kT) ~ 1 - ΔE/kT

ΔE small so can make approx, and population difference is minimal

Therefore insensitive technique

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

How does population difference of spin states effect sensitivity and how is it effected by field?

A

Net absorption depends on difference in population - therefore NMR insenstitive

Population diff inreases with B or γ, and decreasing temperature

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

What is the origin of shielding?

A

Orbiting e- creates magnetic fields which can oppose or reinforce B0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

What is difference in energy and transition freq including shielding?

A

ΔE = hbar γB0 (1-σ)

v = B0γ(1-σ)/2π

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

What is lenz’ law?

A

ε = -N(ΔφB/Δt)
Induced emf gives rise to a current whose mag field opposes original change in flux (is why -ve)

where ε is emf, and the next part is change in flux

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

What is diamagnetic and paramagnetic shielding?

A

Diamagnetic - opposes B and so causes shielding, due to spherical charge distribution

Paramagnetic - can add to B so deshield, due to non-spherical charge distribution

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

What is the Lamb formula for diamagnetic shielding?

A

σd = (μ0e2/3me) ∫ rρ(r) dr
where ρ(r) is e- density

Assumes spherical elec distribution

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

What are some features of diamagnetic shielding?

A

Caused by spherically distributed ground state atom/molecules (from s orbitals)

Opposes B0

Proportional to e- density
1/r dependence

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

What are some features of paramagnetic shielding?

A

Caused by non-spherical distribution, from p and d e-

Augments B0 (is -ve)

Proportional to 1/ΔE and 1/r3

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

What is chemical shift?

A

Measure to relative inner standard (usually TMS)

δ = 106(σref - σ) = 106 (v-vref)/vref

Independent of B0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

How does paramagnetic cause different shifts in TM complexes?

A

Paramagnetic shielding dominates, proportional to 1/ΔE
where ΔE is usually between t2g and eg

As stronger field ligands then smaller chemical shifts

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

What are some contributions to shielding other than dia/para?

A

Neighbouring group anisotropy
Ring current effects
Elec effects
Intermolecular interactions - H bonds, solvent interactions, etc.

H is e- poor and ΔE large so must consider these effects

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

What is anisotropy?

A

Property of being directionally dependent
Includes p,d, and f orbitals

Opposite is isotropy

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

What is magnetisation dependent on?

A

M = χ H

where M is magnetisation, H is magnetic field strength, χ is susceptibility

χ is directionally dependent so magnetisation is too
chemical shielding of nucleus hence depends on it too

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

What are neighbouring group contirbutions?

A

Occur due to currents induced in nearby groups of atoms

Effect is shield/deshield nucleus depending on geometry of group/nucleus

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

How is a point dipole different in each axis?

A

Bμy = 0

Bμz is where the spin is quantised

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
What is μpar and μper?
μpar is parallel to symm axis (z), and is larger μper is perpendicular to symm axis (z)
26
How do ring currents cause shielding/deshielding?
27
What is the neighbouring group anisotropy in alkynes?
28
What is the neighbouring group anisotropy in alkenes?
Protons are deshielded Above/below is shielded
29
What is the shielding that occurs due to ring currents from an aromatic ring?
Protons above/below ring shielded Protons in plane of ring are deshielded
30
What are electric effects in chemcial shielding?
Charged/polar groups modify diamagnetic and/or paramagnetic currents by polarising local e- distributions and perturbation of ground and excisted state wavefn
31
What occurs to give splitting due to scalar spin-spin proton coupling?
32
What is the E difference between two spin-spin coupled atoms?
If two nuclei A and X E = hJAXmAmX where J is spin-spin coupling const (can be +ve or -ve)
33
What is the spin-spin coupling const proportional to?
J α γA γX γ can be +ve/-ve, so J can be too
34
What is the splitting for A and X nulcei? | Weak coupling regime
35
How does J relate to Δv for two nuclei in different regimes?
Weak coupling: JAX << |vx - vA| Mag equivalent: JAX > |vx - vA| Strong coupling: JAX >= |vx - vA|
36
What is chemical equivalence?
2x nuclei which are: 1. spins of same isotopic species 2. molec symm which exchanges two spins
37
What is magnetic equivalence?
Nuclei which are: 1. Chemically equivalent AND one of all coupling const of nucleus i and j with all other nuclei of molecule l (this is an L) Jil (that is an L) = Jjl OR No other spins in the molecule
38
What are the eigenvalues and splitting in weak coupling limit?
Result is two doublets
39
What are the eigenstates when there are equivalent nuclei?
ΔS = 0 means only two energy differences with the same frequency, gives one peak
40
What is the hamiltonian for a two spin system (I and S)?
H^ = -ωII^z - -ωSS^z + (2πJ/hbar) **I^ . S^** Where first two terms are interaction with field and 3rd is the interaction with eachother | Remember I is uppercase i
41
What is the dot product of two spins **I^.S^**?
**I^.S^** = I^xS^x + I^yS^y + I^zS^z = 1/2(I^+S^-) + 1/2(I^-S^+) + I^zS^z
42
How do you show the ket of a two spin system?
First term in ket is I and second is S States include: |αIαS> |αIβS> |βIαS> |βIβS>
43
How do operators I^z and S^z act on kets?
Where the ket doesnt matter I^z|> = +1/2 | > S^z|> = -1/2 | >
44
How do the operators I^+/- and S^+/- work on different kets?
I^+|αI> = 0 I^-|αI> = |βI> S^+|βS> = |αS> S^-|βS> = 0
45
What are the eigenstates in the strong coupling case?
|4> = |βIβS> |3> = -sinθ|αIβS> + cosθ|βIαS> |2> = cosθ|αIβS> + sinθ|βIαS> |1> = αIαS>
46
What is the coupling parameter?
tan2θ = J/δ when θ=0 then is no coupling and when θ=3π/4
47
What are the transitions seen in strong (or general) coupling?
Gives roofing
48
What is the permutation operator and how is used for mag equivalent?
P^12 the hamiltonian for two mag equivalent nuclei (1&2) will remain unchanged Exchange labels of two nuclei and then see what occurs
49
What is the fermi contact interaction?
Is the origin of spin couplings Mag interaction between an e- and an atomic nucleus Crucially dependent upon s-electron char of ground and 1st excited state
50
How is 3J dependent on dihedral angle?
3J = A + Bcosθ + Ccos2θ This is karplus relationship
51
How is the fermi contact interaction dependent on mag field and tumbling?
Mag field - not affected by strength or direction, so independent of spec frequency Isotropic - no dependence on molec tumbling
52
What is the range of 1J C-H coupling?
100-250 Hz
53
What does through space coupling occur in solution and solid?
Solution: anisotropic quantity averages out due to tumbling Bμx =! Bμy =! Bμz Solids: doesn't average out, leads to ∫ (3cos2θ-1)sinθdθ for (3cos2θ-1) = 0, then θ=54.7 which gives a singlet
54
What does the notation KAX denote?
Splitting in spectrum of X caused by dipolar coupling to A
55
What does the fourier transform do?
Converts spectra from time to frequency domain Results in product function which in peaks rather than a progression
56
How does the life-time of a signal determine the signal broadness?
Signal broadens as lifetime decreases
57
What are the advantages of fourier-transform NMR?
* Increased sensitivity * Time saved means more spectra can be done and better signal:noise * Allows for using pulse-sequences
58
What occurs during a pulse to spin states?
Phases of spins are random initially random Mag field aligns the spins
59
What is a rotating frame?
View spins from a frame that rotates with the field Means the view is an apparent static field
60
Why is a rotating frame required?
Freq of applied RF-field B1(t) close to spin resonance freq The effect of the pulse tilts magnetisation vector away from z axis B1(t) oscillates itself so rotating frame to view B1(t) required
61
How does the rotating frame work?
Detail linear field as sum of counter-rotating circularly polarised components Only component that rotates in same sense as Larmor preccesion of the spins is retained
62
What occurs to magnetisation during a pulse in the rotating frame?
Rotates about z-axis with ang freq ωrf, a field **B1**
63
What is nutation freq?
Angular freq of precession ω1 = -γB1
64
What is the angle through which M rotates?
β = -ω1tp where tp is the length of pulse
65
What is a 90-degree pulse?
66
What is a 180-degree pulse?
67
How do spins cause coherence?
Coherent EM radiation induces coherence amongst spins and causes orientations of individual mag moments in the x-y plane to not be random
68
What is relaxation in NMR?
The population after a pulse returning to thermal eqm
69
How does magnetisation increase with time?
Mz(t) = Meq (1 - exp[-(t-ton)/T1] where T1 is the spin-lattice or longitudinal relaxation time in same direction as field (z)
70
How does magnetisation decreases to eqm?
Mz(t) = Meq (1 - exp[-(t-toff)/T1] where T1 is the spin-lattice or longitudinal relaxation time in same direction as field (z)
71
What is the dependence of emission (relaxation) in NMR?
From Einstein coefficient: A α v3 Therefore very slow for NMR
72
How does magnetic interactions effect spin-lattice relaxation?
Instant local mag field might induce a radiationless transition if @ correct freq Therefore can cause spin-lattice relaxation
73
What is rotational correlation time, τc?
Time taken for root-mean-square deflection of the molecules to be about 1 radian t << τc - close to original position t >> τc - lost all memory of position
74
What is τc-1?
Root-mean square rotational frequency to reach 1 radian
75
What is spectral density function, J(ω)?
J(ω) = 2τc/(1 + ω2τc2) Chance that molecular tumbling leads to right freq to make a transition between energy levels
76
What is the plot of spectral density function and tumbling rate?
Intermediate tumbling causes fastest relaxation
77
What does spin-lattice relaxation time, T1, depend on?
Prob that local mag fields are oscillating at resonant NMR freq J(ω)
78
What is spin-spin relaxation time, T2?
Time quantifies rate of decay of manetization within xy plane Doesnt affect total amount of z-magnetization
79
How do T1 and T2 depend on τc?
Same when fast tumbling wrt frequency T1 >= T2 As full magnetization along z cannot be recovered unless all phase coherence has gone with T2
80
What is observed orbital-wise when I > 1/2?
Nucleus possesses an electric quadrupolar moment additional to magnetic dipole moment Leads to distribution of nuclear charge being ellipsoidal, so elec energy varies with orientation
81
What do electric quadrupoles interact with?
Interacts with field gradients NOT with uniform elec field
82
What occurs to quadrupolar interaction in high symm?
High symm environ causes electric field gradients to cancel Means no net quad interaction, so no effect seen
83
How does quadrupolar effect spins?
Induces spin relaxation so causes line broadening Loses multiplet splitting
84
How can you measure spin-lattice relaxation?
Inversion-recovery experiment
85
What is the pulse sequence in an inversion-recovery experiment?
Can measure τ1,2,3,4 Plot NMR signal vs τ
86
How can you get T1 from an inversion-recovery measurement?
Plot ln[I - I(τ)] against τ where I is the fully relaxed signal intensity Then use following to get T1: Mz(τ) = M0(1-2exp[-τ/T1])
87
How can you measure the spin-spin relaxation time (T2)?
Spin-echo experiment
88
What is the pulse sequence in a spin-echo experiment?
89
What is the intensity of signal from a spin-echo experiment?
I(2τ) = I(0) exp(-2τ/T2)
90
How does relaxation change the echo amplitude?
Random mag fields destroy phase coherence (which due to random molec motion) Not refocused by p pulse
91
What is the equation for line broadening according to spin-lattice relaxation?
Δv = 1/πT1
92
What is the line broadening due to spin-spin relaxation?
Δv = 1/πT2
93
What occurs to broadening at slow exchange rate?
Δv = kex = 1/πτ 2 separate sharp peaks observed
94
What occurs to line broadening in intermediate exchange?
kex = πδv/Sqrt[2] ~ 2.2δv A broad peak is observed (two lines merged)
95
What occurs to line broadening in fast exchange?
Δv = π(δv)2/2kex = (π/2)(δv)2τ Gives one sharp line (for two environments)

Year 3 - Chemistry (12 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2025 Bold Learning Solutions. Terms and Conditions