NMR Lecture 1

Question 1

Describe how a nucleus’s magnetic moment is related to its spin quantum number and gyromagnetic ratio.

Answer 1

P = ℏ ⋅ [I(I+1)]^1/2
P = magnitude of intrinsic angular momentum
I = spin quantum number (half integer for particles like electrons and either or for nucleons)
ℏ = Planck’s constant/2pi

μ = γ⋅P
μ = magnetic moment
γ = gyromagnetic ratio

μ = ℏγ ⋅ [I(I+1)]^1/2

The magnetic moment of a nucleus describes the strength and direction of the magnetic field associated with the nucleus when it is placed in an external magnetic field. The interaction of atomic nuclei with external magnetic fields is utilized for analytical and medical purposes.

Question 2

Identify the NMR behavior (active vs. inactive) and spin quantum number of a nucleus based on its atomic number and spin quantum number.

Answer 2

If both mass # and atomic # are even, spin quantum number is 0 and therefore inactive NMR.
If mass # is even and atomic # is odd, spin quantum number is a positive integer and NMR is active.
If mass # is odd, spin quantum number is a half integer and NMR is active.

Question 3

What are some examples of elements with a half integer spin quantum number?

Answer 3

Proton (1H)
Carbon with mass 13
Nitrogen with mass 15
Phosphorus with mass 31

Question 4

Describe how a nucleus’s larmor frequency is related to its gyromagnetic ratio and magnetic field.

Answer 4

ω = -γ ⋅ B
The negative sign indicates that the precession of the nuclear magnetic moment is in the opposite direction to the applied magnetic field.

Question 5

Describe the Zeeman effect. Know how to relate the energy difference between two states of a spin 1/2 with its larmor frequency or gyromagnetic ratio.

Answer 5

The Zeeman effect is the splitting of atomic energy levels in the presences of an external magnetic field.

Question 6

The resonance frequency of which nucleus is the magnetic field strength of an NMR spectrometer referred to?

Answer 6

1H precession in the magnetic field

Question 7

Describe the limiting factors for the sensitivity of NMR method.

Answer 7

number of nuclei in the alpha and beta state

deltaE is small, so the populations of alpha and beta states are nearly equal

Question 8

Describe the factors that affect the macroscopic (net) magnetization.

Answer 8

1) magnitude of the static magnetic field
2) identity of the nucleus
3) temperature
4) number of nuclei

Question 9

Describe the difference between rotational frame and laboratory frame in NMR measurements.

Answer 9

Rotational frame: makes the magnetic field appear constant because we are spinning with it

laboratory frame: nuclear spins precess around the direction of the static magnetic field.