Fundamentals of Magnetic Resonance

Question 1

What is the nuclear spin quantum number

Answer 1

I - describes the intrinsic spin of the nuclei

Question 2

What is the nuclear spin quantum number associated with the z-component?

Answer 2

m - values range from +I to -I in steps of 1

Question 3

What types of nuclei have spin magnetic moment?

Answer 3

Nuclei with nuclear spin > 0

Question 4

What is the Zeeman interaction?

Answer 4

The nuclear magnetic moment will interact with any applied magnetic field. The energy of this interaction can be described by the Zeeman Hamiltonian

Question 5

What can be used to determine the transition frequency from one spin state to another

Answer 5

𝛥E between spin states

Question 6

Limitations of the energy level picture of NMR

Answer 6

NMR is not emission/ absorption spectroscopy, it is a resonance technique

Question 7

What are vectors

Answer 7

Vectors are quantities with both magnitude and a direction defined in terms of a coordinate system

Question 8

What is torque

Answer 8

A twisting force that acts perpendicular to interacting vectors - this causes M to precess around B

Question 9

Net magnestisation

Answer 9

vector sum of all magnetic moments of all spins in sample

Question 10

In absence of magnetic field what is what is the net magnetisation?

Answer 10

zero - no net magnetisation as there is no preference for direction so they all cancel out

Question 11

What happens when 2 magnetic moments are out of phase?

Answer 11

Mostly cancel each other out - destructive interference

Question 12

What happens when 2 magnetic moments are in phase?

Answer 12

The magnetic moments add up - constructive interference

Question 13

When can there only be net magnetisation in Mxy plane

Answer 13

if there is phase coherence - when nuclear magnetic moments precess in sync with one another at same frequency and same initial phase

Question 14

What is the net magnetisation in Mxy plane at thermal equilibrium?

Answer 14

At thermal eqm all spins point in arbitrary directions so Mxy = 0 as there is no phase coherence

Question 15

What happens when we rotate net magnetisation (Mo) into xy plane

Answer 15

Magnetic moments are precessing in sync so add up in xy plane Mxy > 0
Destroy longitudinal magnetisation Mz now = 0 equal popn between energy states
Mo precesses around Bo at Larmor frequency

Question 16

How do we rotate Mo into xy plane?

Answer 16

Generate RF pulse - an oscillating voltage passed through a coil of wire will generate oscillating magnetic field
Radio frequency pulse at Larmor frequency to induce transitions between 2 energy states.
New magnetic field B1 oscillates at larmor frequency perpendicular to Bo

Question 17

What does applying a second magnetic field B1 on x axis perpendicular Bo do?

Answer 17

This causes Mo net magnetisation to precess around B1 in the rotating frame. If we apply the pulse for exactly the right amount of time we can rotate magnetisation from z into xy plane

Question 18

What is NMR receptivity?

Answer 18

NMR receptivity is a measure of how easy it is to detect the NMR signal of a given nucleus - it is quoted relatitive to another nucleus e.g. 1H or 13C

Question 19

Longitudinal relaxation

Answer 19

T1
This process generates the eqm population difference across zeeman energy levels and establishes Mo along z axis

Question 20

Transverse relaxation

Answer 20

T2
process that causes xy magnetisation to decay to zero. Mxy comes from phase coherence so relaxation must be due to loss of phase coherence - randomisation of phase

Question 21

What is the rate of change of longitudinal magnetisation proportional to?

Answer 21

Proportional to the difference between current magnetisation and equilibrium magnetisation

Question 22

what is it called if Mz is larger than equilibrium magnetisation?

Answer 22

Hyperpoarisation
Mz will decay time due to T1 relaxation

Question 23

what is the rate of transverse relaxation proportional to?

Answer 23

magnetisation in xy plane, Mxy

Question 24

What is the rate of longitudinal relaxation proportional to?

Answer 24

The difference between current magnetisation and eqm magnetisation

Question 25

What is effective transverse relaxation T2*?

Answer 25

the rate at which transverse magnetisation decays faster than expected in NMR experiments Mxy can also decay due to reversible dephasing - this comes from nuclei experiencing different larmor frequencies (e.g. bubble in NMR tube) If nuclei in different parts of sample will experience different fields so precess at different frequencies and dephase as time goes on

Question 26

What effect does short T2* have on NMR spectra?

Answer 26

Short T2* (fast relaxation) leads to broad peaks in NMR spectrum - reduced resolution and signal to noise ratio

Question 27

What effect does long T2* have on NMR spectra

Answer 27

This means slow relaxation which leads to narrow peaks with higher signal

Question 28

What is shimming?

Answer 28

Shimming is the process of improving the homogeneity of Bo by applying small additional fields to cancel out small variations across the sample

Question 29

What causes T1 relaxation?

Answer 29

Exchange of energy with the environment re-establishing the equilibrium population difference across the nuclear spin energy levels

Question 30

What causes T2 relaxation?

Answer 30

Interaction between spins and the environment - doesn't require exchange of energy. Causes loss of phase coherence between precessing spins

Question 31

What is dipole-dipole coupling?

Answer 31

direct magnetic spin-spin interaction between nuclei, occurs through space the size of the interaction is determined by the coupling constants As it is an anisotropic interaction it averages out in liquids

Question 32

What is J coupling

Answer 32

indirect magnetic spin-spin interaction mediated by the electrons, occurs through chemical bonds

Question 33

What is Quadrupolar interactions?

Answer 33

Electronic interaction of electric quadrupole moment (eQ) of spins with I > 1/2 with surrounding electric field The more anisotropic the distribution of charge the larger the eQ

Question 34

What are hyperfine interactions?

Answer 34

Interaction between a nuclear spin and an unpaired electron spin, similar in origin to J coupling

Question 35

What makes an interaction an isotropic interaction?

Answer 35

The size of the interaction is independent of the relative orientation of the molecule and the magnetic field

Question 36

Some examples of isotropic interactions?

Answer 36

J coupling Hyperfine Zeeman interaction isotropic chemical shift

Question 37

what makes an interaction an anisotropic interaction

Answer 37

The size of the interaction depends on the orientation of the molecule with respect to the magnetic field

Question 38

Example of anisotropic interaction

Answer 38

Dipole-dipole coupling Quadrupole coupling Chemical shift anisotropy

Question 39

What are the effects of anisotropic interactions on NMR spectra

Answer 39

Cause different frequency shifts depending on orientation of molecule relative to Bo (Not observed in liquid due to molecular tumbling - anisotropic interactions average to zero)

Question 40

What does the size of J-Coupling depend on?

Answer 40

Gyromagnetic ratio of each nucleus number of bonds/ bond angle between nuclei

Question 41

What is chemical equivalence?

Answer 41

Where 2 spins have the same chemical shift, appears as a singlet, no coupling between A and B is observed

Question 42

when are two nuclei magnetically inequivalent?

Answer 42

if they couple differently to a 3rd nucleus. For example in an octahedral complex one H couples cis to a P spin up nuclei and one H couples trans to the same P spin up nuclei

Question 43

If the difference in chemical shift of 2 nuclei is much bigger than the J coupling

Answer 43

get weak coupling standard multiplets

Question 44

If the difference in chemical shift is approximately the same as the J value

Answer 44

Means there is strong coupling Lots of roofing

Question 45

If 2 nuclei have the same chemical shift?

Answer 45

they are chemically equivalent - see a singlet

Question 46

What is chemical shift anisotropy

Answer 46

in the presence of a strong applied field, the electrons in the molecule give rise to a small induced field at the nucleus that opposes Bo

Question 47

What do hyperfine interactions cause in NMR spectroscopy?

Answer 47

causes fast T2 relaxation meaning NMR spectra can often not be obtained for paramagnetic species

Question 48

What is magic angle spinning

Answer 48

Technique used in solid state NMR to average out anisotropic interactions to simplify spectra and recover isotropic chem shift info Averages out anisotropic interactions in a similar way to motional averaging but not random, it is at a fixed rotation frequency at a single specific axis. Rotation axis oriented at 54.7 bc due to symmetry the dipole dipole and CSA interactions are zero at this angle