NMR4

Question 1

What is product operator formalism in NMR?

Answer 1

Product operator formalism is used to describe the evolution of spin states during an NMR experiment. It tracks how magnetization behaves under radiofrequency (RF) pulses, chemical shifts, and scalar couplings, using a set of standardized spin operators.

Question 2

What happens to M_z ​ after a 90° pulse along the y-axis?

Answer 2

It is rotated into the +x-direction:
M_z-> M_x

Question 3

What happens to M_z ​ after a 90° pulse along the x-axis?

Answer 3

It is rotated into the -y-direction:
M_z-> -M_y

Question 4

What happens to M_z ​ after a 90° pulse along the - y-axis?

Answer 4

It is rotated into the -x-direction:
M_z-> -M_x

Question 5

What happens to M_x ​ after a 90° pulse along the y-axis?

Answer 5

• It is rotated into the -z-direction:
  M_x-> -M_z

Question 6

What happens to M_x ​ after a 90° pulse along the x-axis?

Answer 6

• It stays unchanged due to no force applied:
  M_x-> M_x

Question 7

What happens to M_z ​ after a 180° pulse along the x-axis?

Answer 7

• It is rotated into the -z-direction:
  M_z-> -m_z

Question 8

What happens to M_z ​ after a 180° pulse along the y-axis?

Answer 8

• It is rotated into the -z-direction:
  M_z-> -m_z

Question 9

What happens to M_y ​ after a 180° pulse along the x-axis?

Answer 9

• It is rotated into the -y-direction:
  M_y-> -m_y

Question 10

What happens to M_y ​ after a 180° pulse along the -y-axis?

Answer 10

• It stays unchanged:
  M_y-> -m_y

Question 11

In the right-handed coordinate system, the magnetization vector is rotating…

counter clock-wise/clock-wise

… around the magnetic field component of the radiofrequency pulse.

Answer 11

counter clock-wise

Question 12

Iz is exposed to a (90°)y pulse:
What is the resulting magnetization?

Answer 12

I_x

Question 13

When Iz is exposed to a (120°)x pulse, you will get a magnetization vector somewhere in the yz plane, that can be described by:

a * Iz + b * Iy

where a2+b2=1

What is the value of a (give three decimals)?

Answer 13

-0.500

Question 14

When Iz is exposed to a (120°)x pulse, you will get a magnetization vector somewhere in the yz plane, that can be described by:

a * Iz + b * Iy

where a2+b2=1

a is -0.5
What is the value of b (give three decimals)?

Answer 14

-0.866

Question 15

What happens to magnetization at equilibrium when a decay time τ is applied?

Answer 15

At equilibrium, the magnetization vector M⃗ is already stable, aligned with the magnetic field (along the z-axis). If no external pulse is applied and you simply wait a time τ, then nothing happens

Question 16

What happens to magnetization at non- equilibrium when a decay time τ is applied?

Answer 16

It will continue to rotate

Question 17

What is the formula for chemical shift evolution, when you start in x?

Answer 17

M_x→^τ M_x∗cos⁡(ωτ)+M_y∗sin⁡(ωτ)
Here ω=2∗π∗v
This formula is specific for when you start in x but can be appilied anywhere else. Although it should be remembered that the M after the + should be the next axis during rotation. fx for −M_y it should be M_x

Question 18

What is single quantum coherence?

Answer 18

Magnetizations with only one x-y term (I_x,I_y, I_x S_z, I_y S_z, I_x S_z T_z U_z)

Question 19

What is double quantum coherence?

Answer 19

Magnetizations with 2 x-y terms
(I_x S_y, I_x S_x, I_x S_y T_z)

Question 20

What is a tripple quantum coherence?

Answer 20

Is terms that have 3 x-y terms (I_x S_y T_x)

Question 21

What is a zero quantum coherence?

Answer 21

It is magnetization terms with no x-y terms (I_z, S_z, I_z S_z)

Question 22

What is the rule of quantum coherences?

Answer 22

You can record single quantum coherences, but will not record any of the rest. This due to single quantum coherences processed with the frequency of the nucleus. The others dont process with the right frequency and zero coherence dont processes at all.

Question 23

Pick all the product operators describing antiphase magnetization:

I_z
I_-x
2I_zS_x
I_zS_z
-4I_xT_zS_z
2I_xS_-x

Answer 23

2I_zS_x and -4I_xT_zS_z

Question 24

Pick all the terms describing observeable magnetization:
2IxSz
2IySz
2IzSz
Ix
I-z
2IxSy
2IxSx
4IxSzTz

Answer 24

2IxSz , 2IySz , I_x , 4IxSzTz

Question 25

What is the purpose of spin echo?

Answer 25

To refocus dephasing caused by inhomogeneities in the magnetic field. This restores signal lost due to differences in local magnetic environments, without eliminating intrinsic chemical shift information.

Question 26

What special for spin-echos for INEPT calculation?

Answer 26

- If a spin-echo takes place chemcal shift evolution is ignored, so only scalar coupling is necessary to calculate - This simplification is crucial for transferring polarization efficiently from a sensitive nucleus (like ¹H) to a less sensitive one (like ¹³C or ¹⁵N).

Question 27

Is −2H_z C_y a carbon or hydrogen spectra?

Answer 27

It is a carbon spectra because it is the C who contaions the x-y term

Question 28

What is the benefit of a INEPT sequence?

Answer 28

INEPT increases the carbon signal by transferring polarization from hydrogens, which are easier to detect because they are more abundant and have a higher gyromagnetic ratio than carbons. This makes the carbon signal up to 4× stronger. However, INEPT produces antiphase signals that aren't directly detectable. Refocused INEPT is used to correct this.

Question 29

What is the concept of refocussed INEPT?

Answer 29

The concept is to apply an extra 180 degree tau period to turn the antiphase magnetization to inphase magnetization. In this method quatinary carbons are lost.

Question 30

Nævn huskeregler for cos og sin

Answer 30

- Cos^2(x)+sin^2(x)=1 - Cos(x)+sin(x)=sqrt(2)*sin(x+π/4) - (cos(x)+sin(x))^2=1+sin(2x) - (cos(x)-sin(x))^2=1-sin(2x)